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Measurement of muonic hyperfine transition rates and muon capture yields in light nuclei Stocki, Trevor John 1998

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MEASUREMENT OF MUONIC HYPERFINE TRANSITION RATES AND MUON CAPTURE YIELDS IN LIGHT NUCLEI By Trevor John Stocki  B.Sc. (Hons), University of Alberta, 1991 M.Sc, University of Alberta, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Physics  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH COLUMBIA  September 1998 © Trevor John Stocki, 1998  In  presenting  degree  this  at the  thesis  in  University of  partial  fulfilment  of  of  department  this or  thesis for by  his  or  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  representatives.  an advanced  Library shall make it  agree that permission for extensive  scholarly purposes may be her  for  It  is  granted  by the  understood  that  head of copying  my or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department  of  P h V  SijJ  The University of British Columbia Vancouver, Canada  DE-6 (2/88)  Abstract The muonic hyperfine transition rates were measured in LiF, (CF ) , Na, NaH, Al, 2  n  LiAlH4, and for the first time in K and P. These measurements were performed by detecting neutrons via liquid scintillators. No chemical effect was observed when comparing the transition rates in LiF and (CF ) , Na and NaH, Al and LiAlFL,. In the 2  n  case of P and K the newly measured hyperfine transition rates are 48 ± 5 us"' and 25 ± 15 us" respectively. 1  Nitrogen should not have a hyperfine transition if the only hyperfine transition process is through Auger emission, because the hyperfine splitting energy is smaller than the energy needed for the Auger process. So confirmation of a previous nonzero measurement of a hyperfine effect in N was attempted. This search for a hyperfine effect in N was performed by detecting neutrons and y-rays in two separate experiments. In the neutron experiment liquid scintillators were used to measure the time spectra of electrons and neutrons. It was found that the muon lifetime obtained from the neutron time spectrum was different than the lifetime measured in the electron time spectrum. This difference may indicate a hyperfine transition in nitrogen. In the case of the y-ray experiment, which was performed by using two high purity germanium detectors, the results lacked sufficient statistics. During this nitrogen y-ray experiment, much new information was obtained. The yields of y-rays produced from muon capture in N were measured. Previously only the 14  yield from one y-ray had been measured. In this experiment yields for three y-rays in C , 14  three y-rays in C , one y-ray in C , and two y-rays in B were measured. From these l3  l2  l 0  yields, the nuclear level yields were obtained. In addition, the energies of two y-rays in l4  C were measured more accurately than before; these y-rays are at energies of  7016.8 ± 1.3 keV and 6730.6 ± 1.0 keV.  in  Table of Contents Jl  ABSTRACT TABLE OF CONTENTS  :  TABLE OF FIGURES TABLE OF TABLES  :  IV  :  '.  VI  ,.  '.. V I I  ACKNOWLEDGEMENTS  VIII  C H A P T E R 1: I N T R O D U C T I O N 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8  1  :  THE MUON: " W H O ORDERED THAT?" EXOTIC ATOMS THE MUONIC HYPERFINE TRANSITION THE WEAK INTERACTION THE WEAK INTERACTION HAMILTONIAN THE WEAK COUPLING CONSTANTS ALLOWED MUON CAPTURE TRANSITIONS IN GOALS OF THE EXPERIMENTS  :  1 5 10 18 20 23 28 31  '.  •. '. I 4  .': N  :  :  :  C H A P T E R 2: P R E V I O U S E X P E R I M E N T S .  ,  33  2.1 PREVIOUS MUONIC HYPERFINE TRANSITION RATE MEASUREMENTS USING LIQUID SCINTILLATORS '.: . '. :.' 2.2 PREVIOUS MUONIC HYPERFINE TRANSITION RATE MEASUREMENTS USING GERMANIUM DETECTORS : ...... '.  33 34  2.3 PREVIOUS MUONIC HYPERFINE TRANSITION RATE MEASUREMENTS USING MUON SPIN ROTATION (II"SR) .' 2.4 PREVIOUS MEASUREMENTS OF H" N PARTIAL CAPTURE RATES..... 2.5 ANCILLARY REACTIONS : .". :  35 38 39  1 4  ,  '.:  CHAPTER3: DESCRIPTION OF EXPERIMENTS.. 3.1 MUON BEAM PRODUCTION '. : - 3.2 BEAM TELESCOPE AND TARGETS : ..: . 3.3 NEUTRON EXPERIMENTAL SETUP 3.4 THE GAMMA RAY EXPERIMENTAL SETUP 3.5 BEAM TELESCOPE ELECTRONICS 3.6 NEUTRON DETECTOR ELECTRONICS 3.7 THE NEUTRON STROBE ELECTRONICS 3.8 GERMANIUM EXPERIMENT DETECTOR ELECTRONICS 3.9 GERMANIUM EXPERIMENT STROBE ELECTRONICS 3.10 DATA ACQUISITION  46 :.. .'.  : '.  C H A P T E R 4: A N A L Y S I S O F T H E D A T A 4.1 4.2 . 4.3 • 4.4 4.5  How THE NEUTRONS WERE SEPARATED FROM THE GAMMA RAYS AND ELECTRONS How THE HYPERFINE TRANSITION RATES WERE OBTAINED FROM THE NOVEMBER EXPERIMENT How THE NEUTRON.LIQUID NITROGEN HYPERFINE TRANSITION RESULTS WERE OBTAINED ENERGY CALIBRATION OF G E I ..: : HOW THE Y-RAY ENERGY PEAKS WERE FLT ,  46 50 53 55 57 60 64 65 68 70 71 71 73 78 80 83  iv  4.6  How  ti-iE Y-RAY TIME SPECTRA WERE OBTAINED  88  . 4.7  How  THE G E DETECTOR ACCEPTANCES WERE OBTAINED  90  4.8  How  THE Y-RAY YIELDS WERE OBTAINED  '•  CHAPTER 5: THE RESULTS 5.1  •.  97  .:  99  THE HYPERFINE TRANSITION RATE RESULTS FROM THE NEUTRON EXPERIMENT'S  99  5.2 Y-RAVIDENTIFICATIONS AND ENERGIES .  :..J05  5.3 THE Y-RAY TIME SPECTRA RESULTS....:...:...:. 5.4 THE Y-RAY YIELD RESULTS •5.5 THE NUCLEAR LEVEL YIELD RESULTS.  .  .' .:.  120  CHAPTER 6: CONCLUSION REFERENCES  114 117  ;, ..'  127 130  TABLE OF FIGURES FIGURE l . i : FOUR STAGES IN THE FORMATION OF MUONIC ATOMS... .• • FIGURE 1.2: THE OPTIONS OPEN TO THE MUON IN A NUCLEUS WITH NONZERO SPIN FIGURE 1.3: THE'PSEUDOSCALAR MUON CAPTURE REACTION.:  .'  9 13 27  FIGURE 2.1: THE ENERGY SPECTRUM OF N ( 7 i " , y ) ' C [ ] WITH THE POLE TERM SUBTRACTED 14  4  43  9I  FIGURE 2.2: THE ENERGY SPECTRUM OF N ( 7 t \ y ) C [ ] WITH THE POLE TERM AND A RESONANCE IN AT20 M E V AS INDICATED : • FIGURE 2.3: THE ENERGY SPECTRUM-OF N(P,2P) C [ ] FIGURE 2.4: THE PARTIAL ISOBARIC DIAGRAM FOR A =13 (ENERGY IN M E V ) FIGURE 2.5: THE ENERGY SPECTRUM OF N ( P , D ) ' N [ ]. '.. ' FIGURE 3.1: THE T R I U M F BEAMLINES... , FIGURE 3.2: THE M 9 B CHANNEL L 4  U  14  13  I4  92  , 4  94  3  95  C 44 44 45 45 48 49  FIGURES.3: THE COLLIMATOR. ' .• :.-...,...'....:........, 51 FLGURE.3.4: THE BEAM TELESCOPE: COLLIMATOR (BLACK AND GREY); SCINTILLATORS S1, S2, S3 (IN . ORANGE); TARGET (YELLOW); AND MU-METAL SHIELD (BLACK CYLINDER) 51 FIGURE 3.5: THE NEUTRON EXPERIMENTAL SETUP: N1 A N D N 2 (GREEN); N 3 (ORANGE); N 4 (YELLOW); C l , C 2 , C 3 , C 4 , (BLUE); AND THE BEAM TELESCOPE FROM FIGURE 3.4:....• .-. FIGURE 3.6: THE G E EXPERIMENTAL SETUP: G E I AND G E 2 (LIGHT GREEN), C S A AND C S B (GREY CYLINDERS), EL AND E 2 (BLUE), AND THE BEAM TELESCOPE FROM FIGURE 3.4 FIGURE 3.7: THE BEAM TELESCOPE LOGIC FOR THE NOVEMBER AND AUGUST EXPERIMENTS.... FIGURE 3.8: THE BEAM TELESCOPE LOGIC FOR THE MAY EXPERIMENT FIGURE 3.9: THE ELECTRONICS F O R N I : ,  56 58 58 61  FIGURE FIGURE FIGURE FIGURE  3.10: 3.11: 3.12: 3.13:  63 63 64 67  FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE  3.14: THE STROBE ELECTRONICS FOR THE Y-RAY EXPERIMENT 4.1: THE two DIMENSIONAL HISTOGRAM USED FOR NEUTRON DISCRIMINATION...!. 4.2: POSSIBLE N NEUTRON TIME SPECTRA... : ".: 4.3: THE 7010 K E V PEAK DOPPLER FIT 4.4: ONE OF THE 3 DOPPLER FITS TO THE 6092 K E V PEAK. 4.5: ANOTHER FIT TO THE 6 0 9 2 K E V PEAK BUT WITH A FLAT BACKGROUND 4.6: THE DOPPLER FIT OF THE 6092 KEV, SINGLE ESCAPE PEAK 4.7: THE DOPPLER FIT OF THE 3684 K E V PEAK..,.: .: : 4.8: THE G E I EFFICIENCY: :  PULSE SHAPE DISCRIMINATION FOR NEUTRONS AND Y-RAYS THE ELECTRONICS F O R N 3 : :. THE NEUTRON STROBE ELECTRONICS DIAGRAM ELECTRONICS DIAGRAM FOR THE G E SETUP. ..: '.:  :  69 72. 79 • 85 86 86 87 87 95  L 4  • FIGURE4.9: T H E G E 2 ACCEPTANCES...: '..;.:„.: FIGURE5,1: THE TIME SPECTRUM OF LIF, WITH THE DECAY DIVIDED OUT.....; FIGURE 5.2: THE TIME SPECTRUM OF N A , WITH THE DECAY DIVIDED OUT. ....: FIGURE FIGURE FIGURE FIGURE  55  5.3: 5.4: 5.5: 5.6:  THE RESIDUALS OF THE LIF THE RESIDUALS OF THE L I F THE RESIDUALS OF THE N A THE TIME CUTS ON THE G E I  :  ; ',-  :  TIME SPECTRUM WHEN TIME OF FLIGHT WAS FIXED. , TIME SPECTRUM WHEN TIME OF FLIGHTWAS VARIED. TIME SPECTRUM : :.: ROUTER 1 TIME SPECTRUM FOR MUON CAPTURE ON N  96101 :. 101 102 102 103  L 4  • (1 CHANNEL = 4.93 NS):  .'.  :  .'  ••• 106  FIGURE 5.7: THE BACKGROUND SUBTRACTED TIME SPECTRUM FOR THE 3684 KEV Y-RAY,•  115  FIGURE 5.8: THE RATIO OF THE 3684 K E V Y-RAY TO THE ELECTRON TIME SPECTRA  115  FIGURE 5.9: THE BACKGROUND SUBTRACTED TIME SPECTRUM FOR THE 4439 KEV Y-RAY.  116  FIGURE 5.10: THE RATIO OF THE 4 4 3 9 K E V Y-RAY TO THE ELECTRON TIME SPECTRA.  116  FIGURE 5.11: THE NUCLEAR LEVEL DIAGRAM OF C . . . 13  FIGURE 5.12: THE NUCLEAR LEVEL DIAGRAM OF C . L 4  •  125 :  126  Table of Tables T A B L E l . I : PROPERTIES O F T H E M U O N . TABLE  1.2: T H E L E P T O N F A M I L Y  TABLE  1.3: V A L U E S OF- —  ..  4 •.  4  ' • AA F O R T H R E E DIFFERENT M O D E L S .  15  Ac • TABLE  1.4: M U O N I C H Y P E R F I N E V A L U E S FOR SPLITTING E N E R G Y ( e ) , E J E C T E D E L E C T R O N S H E L L , E N E R G Y OF T H A T S H E L L , A N D A  1.5: T A B L E 1.6: T A B L E 1.7: T A B L E 1.8: TABLE  CALCULATED BY WINSTON[ ]:  18  2 6  H  T H E R E L A T I V E S T R E N G T H S OF T H E 4 F U N D A M E N T A L F O R C E S  19,  T H E T H R E E C L A S S E S O F - W E A K INTERACTIONS:  21  . T H E V A L U E S O F THE.COUPLING CONSTANTS  :'.  27  T H E R E L A T I V E C O N T R I B U T I O N S IN % OF T H E V A R I O U S H A D R O N I C W E A K F O R M F A C T O R S F R O M TWO MODELS FOR M U O N CAPTURE ON  M  N (  L 4  N - » C ( 2 1 : 7 . 0 1 M E V ) [ ]. M  +  . . . . 30  23  T A B L E 1.9: .9: M U O N C A P T U R E Y I E L D S A N D PARTIAL C A P T U R E R A T E S T O A L L O W E D TRANSITIONS IN  . '  (TOTAL CAPTURE RATE  is 6.93 x 10 s"'). 4  L 4  C [ ] 74  :  31  T A B L E 2.1: P R E V I O U S M E A S U R E M E N T S OF MUONIC H Y P E R F F N E TRANSITION R A T E S . T A B L E 2.2: T H E PREVIOUS M E A S U R E M E N T S O F P A R T I A L M U O N C A P T U R E R A T E S IN LEVEL....  •..  1 4  4  37 N TO T H E 7010 K E V  :  T A B L E 2.3: T H E T R A N S I T I O N S S E E N F R O M T A B L E 2.4: I N T E G R A T E D  ,  L 4  '.  N(7i\y)' C.[ ] 4  :.. 39  '  9 1  42  N ( Y , P ) C CROSS SECTIONS T O 2 9 M E V f ]...' I 3  43  93  T A B L E 3.1: SIZES O F B E A M T E L E S C O P E SCINTILLATORS ( C M ) T A B L E 3.2: LIST O F T A R G E T S U S E D . . . . . . . . . . . .  52  :  :  :  53  T A B L E 4 : 1 : VALUES O F S A N D X F R O M NONHYPERFINETARGETS  ,  0  74  T A B L E 4.2: V A L U E S O F S A N D X FOR HYPERFINE E L E M E N T S .  •.  0  75  T A B L E 4.3: B A C K G R O U N D C O R R E C T I O N S FOR T H E H Y P E R F I N E E L E M E N T S  78  T A B L E 4.4: T H E ENERGIES O F T H E Y-RAYS A N D X - R A Y S U S E D T O C A L I B R A T E T H E L O W E N E R G Y REGION  OF G E L .  ......  '.'  •.  8I  :  T A B L E 4.5: T H E ENERGIES O F T H E Y-RAYS A N D X - R A Y S U S E D T O C A L I B R A T E T H E M E D I U M E N E R G Y REGION OFGEl  .'..v  "...  82  T A B L E 4.6: T H E E N E R G I E S O F T H E Y-RAYS A N D X - R A Y S U S E D T O C A L I B R A T E T H E HIGH E N E R G Y REGION O F GEI  (THE  T A B L E 4.7: T H E G E I  56  F E ( N , Y ) LINES A R E B A C K G R O U N D , B U T A R E U S E F U L FOR C A L I B R A T I O N ) . ! . : . . . :  E N E R G Y R E S O L U T I O N M E A S U R E D AS A F U N C T I O N OF E N E R G Y  T A B L E 4.8: T H E M U O N I C X - R A Y TRANSITION PROBABILITIES. T A B L E 4.9: T H E A C C E P T A N C E S F O R G E I  :  5.1:  HYPERFINE TRANSITION RATES  .  95  : :  :  96  :  -. 97  (US' ).'  -.  1  T A B L E 5.2: T H E C A P T U R E R A T E A S Y M M E T R Y  82 ;.. 88  :. .-;  T A B L E 4.10: T H E A C C E P T A N C E S F O R G E 2 . . . TABLE  :  :  100  :  103  T A B L E 5.3: M U O N L I F E T I M E S IN N I T R O G R E N A N D O X Y G E N  105.  T A B L E 5.4: T H E D I F F E R E N C E B E T W E E N D E T E C T I N G E L E C T R O N S A N D N E U T R O N S  :  105  T A B L E 5.5: T H E Y-RAYS S E E N IN T H E LOW E N E R G Y R E G I O N O F G E 1  109  T A B L E 5.6:  112  T A B L E 5.7: T A B L E 5.8:  T H E Y-RAYS S E E N IN T H E M E D I U M E N E R G Y R E G I O N O F G E I T H E Y-RAYS S E E N IN T H E HIGH E N E R G Y R E G I O N O F G E L . . . . : . . . . . : . . . . , . . . . 1 4  112  C Y-RAY E N E R G I E S IN K E V ( O N L Y FINAL A V E R A G E S I N C L U D E S Y S T E M A T I C E R R O R S )  T A B L E 5.9: T H E  1 3  C Y-RAY YIELD RESULTS  T A B L E 5:10: T H E  1 4  C Y - R A Y Y I E L D RESULTS  T A B L E 5.11: T H E  1 2  C AND  T A B L E 5.12: T H E  I 0  BE-  I 2  I  0  : '  117 .-  ':  119  B Y - R A Y YIELD RESULTS.  B , AND  L 3  :  B Y-RAY Y I E L D R E S U L T S .  T A B L E 5 . 1 3 : ' T H E N U C L E A R L E V E L YIELDS OF  , 3  C  T A B L E 5.14: T H E N U C L E A R L E V E L YIELDS O F  L 4  C  T A B L E 5.15: T H E N U C L E A R , L E V E L YIELDS O F T A B L E 5.16: T H E N U C L E A R L E V E L YIELDS OF  114  I 0  I 0  BE,  .-..119 ....:  ;  120  ,...:........:  BAND 1 2  1 2  124  C...  B , AND  119  124 , 3  B.  '..  -.  124  vu  Acknowledgements I would like to express my gratitude and appreciation to my supervisor Professor David F. Measday for his advice, guidance, and encouragement throughout this work. I would like to thank Drs. Glen Marshall and Elie Korkmaz for lending liquid scintillators and pulse shape discrimination N I M modules to me, without which two of the experiments in this thesis would not be possible. I would also like to thank my collaborators (E. Gete, M.C. Fujiwara, and Drs. J.H. Brewer, T.P. Gorringe, J. Lange, D.F. Measday, B.A. Moftah, and M . A . Saliba) for their help and advice in running the experiments. I would also like to thank Lars Holm for his help with the University of Alberta pulse shape discrimination N I M module and Dr. A. MacFarlane for his liquid nitrogen .target vessel tips. Iwould also like to thank Nicolas Saurel for his work on data that was not presented in this thesis; through guiding him I was able to rethink some of my own work. I would also like to thank Professors J.H. Brewer, S.E. Calvert, J.P. Deutsch, R.R. Johnson, I.S. Towner, D. Walker and D.L.L. Williams for their advice and detailed reading of the manuscript. I would also like to thank Dr, Larry Lee, Mike Landry, and Ermias Gete for our many enjoyable conversations on various physics topics, while I have been at TRIUMF. The University of Manitoba lunch club (my former collaborators) needs mention, in light of the many interesting lunch time discussions I enjoyed with them. The folks at Digital Accelerator Corporation also need to be thanked for their support. M y wife, Evelyn, needs special thanks for her diligent help in the proof reading of this thesis and in preparing some of the figures. Finally, I would like to thank my parents and my wife for their constant support through out my thesis.  VIII  Chapter 1: Introduction 1.1 The Muon: "Who ordered that?"  1  In 1935, w h e n the o n l y k n o w n b u i l d i n g b l o c k s o f matter were the proton, the neutron, the electron and the positron, Y u k a w a ['] postulated a particle with a mass between the electron and the proton. T h i s particle w o u l d be the carrier o f the nuclear force, i.e. the particle responsible for h o l d i n g the nucleus together.  T h i s Y u k a w a particle  was predicted to have a mass o f a p p r o x i m a t e l y 200 M e V / c . T w o years later A n d e r s o n and N e d d e r m e y e r [ ] m a d e energy loss measurements b y p l a c i n g a 1 c m p l a t i n u m plate 2  into a c l o u d c h a m b e r , w h i c h was in a magnetic field. T h e y f o u n d two event types; i n o n e event type, the particle lost energy in a m a n n e r consistent w i t h the w a y electrons loose energy; in the other event type the particle lost very little energy in the p l a t i n u m plate. T h e s e penetrating particles were heavier than an electron but not as i o n i z i n g as protons. A t the same time Street and Stevenson [ ] reported similar c o s m i c ray results. T h e y m e a s u r e d the m a s s o f these penetrating particles by m e a s u r i n g the m o m e n t u m a n d . • i o n i z a t i o n o f these particles at the same time. T h e y f o u n d that the penetrating particles had a mass o f about 130 times the mass o f the electron (although this is about 1.6 times smaller than the present mass measurement).  C o u l d this particle be the Y u k a w a force  carrier? T h e identification needed to be c o n f i r m e d .  ' Said by 1,1. Rabi upon finding out that the muon was an extra particle.  In 1940, Tomonaga and Arakif ] showed that the positive and negative 4  penetrating particles should have different effects in matter if these particles were the Yukawa.particle. They postulated that the positive particles should come to rest and decay, but the negative particle would be captured into an atomic orbit with small radii, forming an exotic atom. If it were the nuclear force carrier, the penetrating particle would then interact quickly with the nucleus. To test this hypothesis, Conversi et ak |°] used a magnetic field to select either positive or negative penetrating particles from cosmic rays. They found that the positive particles did decay as predicted. When they used an iron absorber, the negative particles did not decay, but were absorbed by the nucleus. However, when they used a carbon absorber, the negative particles decayed. This implied that these particles were not the Yukawa particles. Shortly after those results, D.H. Perkins[ ] used photographic emulsions to look at the cosmic rays. He saw 6  an event in which a penetrating particle stopped and blasted a nucleus into 3 fragments. This was a Tomonaga and Araki type event, which contradicted the results of Conversi et al. Then in 1947, Lattes et al.[ ] examined photographic plates that were exposed in 7  the Bolivian Andes at an altitude of 5500 m and found 40 events in which one penetrating particle decayed into another penetrating particle. Lattes et al. named these two particles the TT and u mesons (they are now called the pion and muon). They found that the pion was slightly more massive than the muon. They postulated that the particle which Perkins had observed was the Yukawa particle or the pion, and Conversi's group was looking at muons. Lattes et al. also observed that the pion decay product, namely the muon, had a fixed range. This implied that the muon was produced at a fixed energy,  2  which in turn implied that the pion decay was a two body decay. They deduced that the second particle was of low or zero mass.and it could be either an electron or a neutrino. Currently it is known that the second particle is a neutrino,' and the pions decay as follows: .  *  .  :  /'  v,  ^  . ('-I)  .  . (1.2)  where v and v• are muon neutrinos and muon antineutrinos. This is the primary way muons are produced and how they were produced for this thesis. Table 1.1 gives the present day characteristics of the muon. The muon is now considered one of six leptons, which are listed in Table 1.2. O f these leptons, the tau neutrino, is the only one which has not been directly observed, although the Donut experiment at Fermilab (E872) has seen 3 candidate events by the use of emulsions[ ]. A 8  lepton is a particle which interacts via the weak force; and i f it has charge, it also interacts via the electromagnetic force. Most of the time the free muon decays in a three body decay:  //  e~ i/. v  «' -•**''>,  (1.3)  .  (1-4)  This three particle decay is consistent with the fact that the energy spectrum of the decay electrons is a continuum. Since the maximum energy of these electrons is 53 MeV, it would: imply that the neutrinos must have either a small or zero mass. The direct limits o'n-neutrino masses are m m  < 4.5 eV/c from tritium p decay experimentsf ] and 2  v  9  < 0.27 MeV/c from pion decay experimentsf ]. For some time there has been a 2  v  10  deficit of solar neutrinos, observed in several experiments. The most popular explanation is that {rn - m )= 10"° eV /c . Recently Super-Kamiokande["] has measured a 2  v  2  2  4  v  zenith angle dependance of muon and electron neutrinos, which implies v <-» v  T  oscillations. The results also imply a mass difference squared (Am ) of 10" e V < A m < 2  3  2  2  10" eV . Thus the most likely explanation is that the mass of the electron neutrino is 2  2  6  2  3  1  2  approximately 10" eV/c , the mass of the muon neutrino is approximately 3 x 10" eV/c , and the mass of the tau neutrino is approximately 5 x 10" eV/c . These masses are riot 2  2  large enough to constitute a significant fraction of the the dark matter of the universe («2 x 10" ). As far as this thesis is concerned, these masses are far too small to be significant, so we can set them all to zero. Spin1.1: Properties " . 'of the muon. Table Mass Charge Mean Lifetime Magnetic Moment  Vi 105.658389 ± 0.000034 MeV/c = e= 1.60217733(49) x 10" C (2.19703 ±0.00004) x 10" s • 1.001165923 ± 0.000000008 e/i/2ra, 2  iy  6  Table 1.2: he lepton family. Charge Particles e ±1 T 0 V u  4  1.2 Exotic Atoms An exotic atom is an atom with an electron replaced by a negatively charged particle. There are five types of exotic atoms: pionic, kaonic, muonic, hyperonic ( I " , Q", and E"), and antiprotonic. As mentioned in Section l . I, Conversi et al. ['] in 1947 saw the first experimental indication of exotic atoms.' In that case it was a muonic atom. 12  13  During that same year, Wheeler [ ] and Fermi and Teller [ ] proposed that exotic or mesic atoms should exist, since the cascade time for the exotic particle was 13  approximately 1.0" seconds, which is a much shorter time than the lifetime of the exotic particle. The first experimental evidence for exotic atoms was by Chang [ ]. He 14  indirectly observed muonic x-rays and muonic y-rays from muonic atoms created by cosmic rays.  •  •'  '  The energy levels of exotic atoms are nominally the same as the levels of the hydrogen atom, except for the fact that the exotic particle (u", rf, K", Q", S", 5", or p ) is much more massive than the electron. This means that energies of the transitions are quite high (of the order of MeV) and the orbits of the exotic particle are much closer to the nucleus by a factor of m /m xotic- The consequence of these tight orbits is that the . e  e  wave function of the exotic particle will overlap significantly with the nucleus. Therefore the exotic particle will interact more readily with the nucleus. At TRIUMF, to artificially form muonic atoms specifically, we produce muohs, which we fire into a target material. The kinetic energy of these muons is around 10 MeV. As they enter the target they are slowed down and scattered by electromagnetic • interactions. These electromagnetic interactions slow the mubns down to 2 keV. This process takes about TO" to 10" seconds in condensed material. The depolarization of 10  9  5  the muon is negligible in this case. Four stages of the life of a muonic atom are'shown in Figure 1.1. Once the muons slow down to 2 keV, the muon can be captured by a nearby atom. The muon is captured into a high orbital angular momentum state and loses approximately two thirds of its polarization. The principal quantum number (n) of this state is approximately 14 ( «  ^/w^T^) O -  n c e  captured in this state an excited muonic  atom is formed. Since the muon mass is 207 times larger than the electron's mass, the muon is actually captured "between" the l'> 0 electron orbits and the nucleus. This process takes about 10" seconds. 14  Since the muonic atom is formed in an excited state (n « 14), the muon will 13  cascade down in 10" seconds to its ground state, namely the Is state (but some times the muon can get trapped in a metastable 2s state for some nuclei). In spinless nuclei this cascade causes the muon to lose approximately half of its remaining polarization. In nonzero spin nuclei the cascade causes the muon to lose even more of its polarization. In the first stage of a cascade the muonic atom de-excites by giving off Auger electrons. Auger electrons are outer atomic electrons, which take the energy released by the muon's transition. These Auger electrons leave the atom in an ionized state. As the muon cascades down, the energy given off in each transition increases to the point where the rate for the Auger effect becomes small compared to the E l X-ray transitions. This is because the Auger transition can only compete with radiative transitions i f the distance between the orbital electrons and the orbital muon is much less than the wavelength of the transition. Since the energy of the transitions increases at small n, then the  wavelength of the transition decreases. So for the rest of trie muon's cascade, X-rays are given off until the muon reaches the Is state. Once the muon reaches the Is state, the muon has 2 options. It can undergo its normal decay into an electron and two neutrinos (see Equation 1.3) or it can be captured by the nucleus. Nuclear capture can be thought of the muon interacting with a bound proton in the nucleus, producing a neutron and a neutrino.  /u~ + p ^.n+  v .- • M  *  (f.5)  .  ' :.  It can also be thought of as interacting with the entire nucleus, leaving the (Z-l) nucleus in an excited state (usually a giant dipole resonance):  //  +(A/Z)~>{A.7.-\)'  +v  fl  . (1-6)  The time the muon spends in the Is state depends on the type of nucleus it is orbiting. If the muon is orbiting a light nucleus, then the rate of nuclear capture will be small and the muon will live for around 2 microseconds. If the muon is orbiting a heavy nucleus like gold, then the rate of nuclear capture is large and the muon will live for as short as 70 nanoseconds. If the nucleus has a magnetic moment (or spin), the Is state experiences hyperfine splitting, and more options are available to the muon. This will be explained in more detail in Section 1.3. The nuclear capture rate depends on the amount of overlap between the nucleus and the orbiting muon. Assuming the nucleus is a point and that all the protons interact  7  independently w i t h the m u o n , Wheelerf "'] came up with a basic m o d e l for the nuclear 1  capture rate:  A ^ E K ( 0 ) f = z | ^ ( 0 ) f =  where T  H  (1.7)  •  an  7.  Q  (0) is the m u o n wave function at the center o f the n u c l e u s , and ao is the B o h r  radius. F o r h i g h Z , m u c h o f the m u o n i c orbital lies within the n u c l e u s , so Z is r e p l a c e d ' by Z ff. T h i s Z ff l a w overestimates the rate in heavy n u c l e i , but is a g o o d a p p r o x i m a t i o n 4  e  e  for light n u c l e i . P r i m a k o f f [ ] came up with a calculation w h i c h was m o r e realistic, in the. sense 16  that it i n c l u d e d the P a u l ; principle so that the limitation i n the available final states f o r the n e w l y t r a n s f o r m e d neutron was taken into account. G o u l a r d a n d P r i m a k o f f T ] have 17  i m p r o v e d the c a l c u l a t i o n to o v e r c o m e a systematic h e a v y element deviation f o u n d i n the original P r i m a k b f f f o r m u l a . M o r e m o d e l s o f the total m u o n capture rate are d i s c u s s e d i n the P h . D . thesis o f S u z u k i [ ] . 18  Energy loss through EM interactions  FIGURE 1.1:  Coulomb field attracts muon ^  FOUR STAGES IN THE FORMATION OF MUONIC ATOMS.  a  e i c W  U t  As indicated above, when the muon is in the Is state, it can decay or be captured. So the total muon disappearance rate is given by  A  r  = A +Q(Z)A c  D  ,  (1,8)  where Q(Z) is the Huff factor that takes into account the fact that the muon is bound in the atom, which in turn causes the decay rate ( A D ) to decrease (by as much as 20% in heavy nuclei). This decrease is primarily due to the fact that the bound muon has less energy available to it than the free muon. The CPT theorem is assumed in order to get the decay rate of the free negative muon from the very precise decay rate of the free positive muon. The muon lifetime in a certain atom is then given by  r =~  .  -  "(1.9)  Suzuki et al. [ ] have measured the muon lifetime in 50 elements and 8 isotopes.. Since I9  then, new measurements have been made for uranium and neptunium [ ]. 20  1.3 The Muonic Hyperfine Transition If the atom that the muon stops in has a nonzero nuclear spin, then the magnetic field associated with this nuclear spin will interact with the orbital electrons and the orbital muons. This interaction causes the electron orbits and the muon orbits to split.  10  The lowest muonic level (or Is level) is split into two levels (F and F") as shown in +  Figure 1.2 (assuming u.| > 0). Thus when a muonic-atom is formed in an atom that has a nonzero nuclear spin, the muon cascades down,to the Is state, which is now split into two levels, F and F". If the muon ends up in the F state it has three options. The first option +  +  is for it to simply decay into an electron and two neutrinos at a rate A D . The second . +  option for the muon is for it to be captured by the nucleus at a rate A c . The third option • +  for the muon is for it to make the hyperfine transition to the F" level at a rate A . In H  making this transition an Auger electron is given off [ ], since the M l photon transition 21  rate is much smaller than A , as calculated by Winston and Telegdi[ ]. This M l photon +  22  D  transition between muonic hyperfine states can be calculated to be  4aV/ R  ?  =  3^(2/  +  l)  .'  1.32xl(rV/ 2/ + 1  .  .  (^omic umts)  (sec , s in eV),'  (1.10)  -1  where I is the spin of the nucleus, and s is the hyperfine splitting energy. This R is at y  least 400 times smaller than the Auger emission transition rate[ J. If the energy 26  difference between the two levels is less then the energy required to give off an Auger electron, then the muon effectively does not have the third option. If the muon is in the F" level, then it only has two options: to decay or to be captured by the nucleus. The Auger emission transitions mentioned above have a Z dependence. Mukhopadhyay[" ] groups these nuclei into four categories: 1) hydrogen isotopes  ll  ( A = 1,2,3); 2) nuclei with no appreciable hyperfine transition (3 < A < 10); 3) nuclei with a hyperfine transition rate AH comparable to AD (10 < A < 40); and 4) nuclei with very fast hyperfine transition rates ( A > 40). In the first category, hyperfine conversion is induced by atomic or molecular collisions. For hydrogen gas at 300K, the conversion time of p~p atoms is 1.2 us at 0.5 atm, and the time is 82 ns at 8 atm[ ]. In liquid hydrogen pup molecules are formed 24  which complicate the measurement of the \xp capture rate. For mixed isotopes, molecules such as pud, dpd, put, dut arid tut form and this induces nuclear reactions such as p + d— > He + y. Details of these complex effects are discussed in the review by 3  Breunlich[ ]. These complications will not be discussed any further in this thesis. In the second category the hyperfine populations are nearly stationary through the passage of time.  12  F  +  f  A!  IS Aii  r  Nucleus  FIGURE l .2: THE OPTIONS OPEN TO THE MUON IN A NUCLEUS WITH NONZERO SPIN.  In the third category Winston[ ] assumes the F~ states are populated statistically at time zero (still assuming pi > 0), the populations in the two states at time zero being given by  » (0) = +  7+1 27 + 1 '  «_«>) =  27 + 1  (1.11)  13  where I is the nuclear spin. He then finds the time spectrum for the capture products to be  =q \ - A e- "' L" -' , •\ /y J  N (t) /y  A  n/  A  (1.12)  where C is a constant and where  •A._=A" +A , C  A . =A;.-:-A,, .  D  (1.13)  The asymmetry is given by  AA A/=«  +  (0)—  ,  (1.14)  where the difference in capture rates is A A = A . - A+. -The value of A A does not have to be the same for neutron and y-ray observations. In other words, there may be branching ratio effects. Winston, also calculated the time spectrum of the decay electrons in a similar manner yielding:  ' N (t) e  = c(l-A e-' "')e~ K  Xj  e  (1.15)  where the asymmetry is given by  14  T h e value o f A  c  is m u c h smaller than A / . w h i c h is a disadvantage for electron detection n  experiments trying to measure A H , but A  y j  c  has the advantage that it has no b r a n c h i n g ratio  effects.  W i n s t o n [ ] discusses three m e t h o d s for the calculation o f = ^ - . 2 6  •  .'  T h e results o f  Ar  these calculations are in T a b l e 1.3. T h e F. averaged capture rate A c is g i v e n by.  A c = n. ( C I A ; . + n ( 0 ) A '  r  .  '  (1.17)  T a b l e 1.3: V a l u e s o f =— for three different models. • • • • Ac ;. Element "B F  i y  2 j  Na  1 1  K\  '  G1  C\ K  4 : ,  Sc  Sly  ]  Primakoff[ T 26  Uberall[ ] 2y  0.51  1.2  .0,42  0.76  0.76  0.18  0.28  0;49  0.25  0.37  0.45  -  -0.09  ir  J 9  2 6  0,14 :  Alp J 3  BLYP[  •  -0.09  -0.14  -0.08  -.0.11  .  0-10 0.09  3 i  Mn  0.06  3 y  Co  0.08  6 j  Cu  0.09  b y  Ga  0.08  "Ga  0.08  / 3  As  0.08  / y  Br  0.07  8 1  Br  0.07  -  0.13 •  15  gees roughly as 2 / Z for odd Z nuclei-because of the  The asymmetry parameter  '  Ac:.  profound spin dependence of the pp interaction; viz. the singlet state has a capture rate of 670 s" whereas the triplet is only 13 s" . Thus one can reckon that only half the core 1  1  protons are contributing to the capture rate and A A is the difference between the triplet and singlet rate for the odd proton. For the odd N nuclei (viz. C , Q , N e , M g , 1 3  l7  2l  2 5  29  Si)  this asymmetry is negligible and the hyperfine transition rate can not be measured from capture effects. Bernstein, Lee, Yang, and PrimakoffT ] (BLYP) have performed a more 27  careful estimate based on this model. They calculated ;  Ar  for a nucleus with odd atomic  number, Z and odd atomic mass, A. They constructed this nucleus as one outside "lone" proton occupying a I1+1/2 orbital and a core of an even number of protons and neutrons. This core is assumed to be spinless and therefore when the muon captures on the core protons, it is independent of I. This implies that the core contributes the same amounts to both Ac' and Ac . They also assumed that this "lone" proton is a free proton. To take +  into account the effect of the Pauli principle, they introduced a factor  The t, factor had  more of an inhibitory effect on the "core" than on the "lone" proton. Most of the uncertainty in calculating came from predicting ^. ' A:: :  The second method of calculating '  Ar  was based on the first method, but had a :  different estimate for c. Primakoff used his closure formulas [ ] to calculate  for a  28  '  :  '  Ac  S1/2 proton (hole) outside (inside) a J = 0, T = 0 nuclear core. This calculation can also be  16  extended to the case of a nucleus with several protons (holes) outside (inside) a J = 0, T 0 core.  • The third method by liberal 1[ ] was to use the shell model wave functions to 29  workout Ac and the hyperfine effects. To calculate the hyperfine transition rates, Winston[ ] first calculated the hyperfine splitting energy (s) for odd Z, odd A nuclei. These splitting energies (along with the one for N ) and the lowest electronic shells the muonic transitions would eject l4  are listed in Table 1.5. The s for N was calculated by Ishida[ ]. For the case in which 14  30  it was borderline whether or not a shell would be ejected, Winston took into account effects on s from the different contributions, of orbital and. spin magnetic moments of the nucleus. It is not certain if these effects were taken into account for N . 14  Winsfon[ ] then calculated the hyperfine transition rate, by.the use of 26  nonrelativistic Hamiltonians for the atomic s-shell and p-shell electrons. He calculated the hyperfine transition rate for each ionizable electronic shell and then summed over the results. Since the hyperfine transition is completely analogous to the internal conversion. of nuclear M l transitions, Winston considered the nucleus and Is muon as a "pseudonucleus". This "pseudonucleus" has a charge of Z'=Z-1 and a combined magnetic moment. For the atomic electrons, this "pseudonucleus" was considered a point. Winston also assumes that the holes created by Auger electrons during the cascade of the muon down to the Is level are refilled rapidly„ If they were not refilled rapidly, then they would decrease the hyperfine transition rate in two ways. The first way would be through the depletion of electrons that would be available to ionize. The second way would be by raising the electron binding energy threshold. To look for this type ofeffect  on the hyperfine transition rate, one of the goals of this thesis was to measure the transition rate in metals and nonmetals. The calculated values of the hyperfine transition rate are also given in Table 1.4.  Table 1.4: Muonic hyperfine values for splitting energy (s), ejected electron shell, energy of that shell, and A calculated by Winston[ ]. 26  H  Element  s (eV)  "B N F Na  18 7.5 126 120 263 190 120 98 72 . 920 1220 995 1450 925 900 1150 720 1150 1200 ,  l 4  i y  ZJ  11  A\  P C1 C1 K Sc V "Mn Co Cu Ga "Ga As Br Br j l  JS  J/  j y  4S  M  i y  b J  b y  /3  /y  s l  Ejected Shell L, None L, Li L, L, M, M, " Mi LJ  L, L, L, L„ Mi L„ Mi MI  M,  •  Energy of Shell (eV) 9.3 11.26 30 40 88.6 150 5 5 35 439 565 699 850 872 132 1040 175 227 227  A H (MS ) -1  0.25 . 0.0 5.8 14 4 1 . 58 8.0 8.0 22 460 700 930 •:. 1300 500 330. 650 430 3400 3400  1.4 The Weak Interaction There are four fundamental forces in nature: gravitational, electromagnetic, weak nuclear and strong nuclear. Table 1.5 shows their relative strengths. O f these only electromagnetism and gravity are experienced in everyday life. The weak interaction is  18  unique in the sense that it violates symmetry principles and conservation rules such as parity conservation, charge conjugation, and time reversal invariance.  Table 1.5: The relative strengths of the 4 fundamental forces. Force Relative Strength Strong Nuclear 1 Electromagnetic Weak Nuclear 10" Gravity ur" 6  In 1934 Fermi[ ] proposed a theory of P decay, which was the first theory of 31  weak interactions. This theory was formulated as a vector type of interaction, which meant that p decay occurs only between nuclear states with identical angular momentum. But it was found that not all p decays occur between states With identical angular momentum. So Gamow and Teller[ ], in 1936, generalized the interaction tb include: 32  vector (V), scalar (S), pseudoscalar (P), axial vector (A) and tensor (T) interactions. The existence of 0 —» 0 and 0 —» 1 P decays implied that at least one of the S and V, Fermi +  +  +  +  type of interactions and at least one of A and T, Gamow-Teller type of interactions were needed for the description of p decay. Which of these combinations of interactions . dominated P decay was not determined until after it was pointed out by Lee and Yang[ ] j3  that there was no evidence in favor of parity conservation in the weak interactions. Lee and Yang suggested this because of the (T - 0) enigma . These two particles, the x and 2  +  the 0 , had the same mass and lifetimes, but their decays were of different parities. If +  2  Note that this is not the same T lepton mentioned in Section 1.1: This T particle is now named the kaon.  19  parity conservation was somehow violated they could be the same particle. In 1956 Wu[ ] found parity violation in the (3 decay of polarized Co, and the x and the Q are 34  60  +  ¥  now considered one particle called the kaon (K ). After the discovery of parity violation +  in Co, it was found that pion and muon decay were also parity violating^ , ]. After 60  3 36  many parity violation experiments (including the work of Winston[ ]) it was found that 26  the weak interaction is a vector minus axial vector (V-A) type of interaction. Presently the weak interaction is part of the Standard Model of Particle Physics, which contains the unification of the weak and the electromagnetic forces (the Weinberg37 38 39  Salam-Glashow electroweak theory[ , , ]). This theory is a renormalizable gauge theory, which has predicted the existence of the neutral weak force carrier Z° boson, which was discovered along with the charged weak force carriers, theW* bosons, at CERN[ , , , ]. 40  41  42  43  1.5 The Weak Interaction Hamiltonian Muon capture at low momentum transfer (q « Mw") is adequately described by the V-A theory as discussed in the last section. The weak interaction Hamiltonian at a four vector space-time point, x, is given by the following current-current form:  H(x)  ! h.c.  = -^J\(x)f(x)  V2  (1.18)  where G = 1.16637(2) x IO" GeV" [ ] is the effective weak interaction coupling 3  2  44  constant, and J^. is the weak current given by  .  20  J Xx) = ;  j" +j[  (1.19)  x  where ix is the hadronic component of the weak current and i\ is. the leptonic component of the weak current. Due to this decomposition, weak interactions can be classified in three ways as shown in Table 1.6.  able 1.6: The three classes of weak interactions. Weak interaction type Particles involved Leptonic Only leptons  Example /'  Semileptonic  Leptons and hadrons.  Hadronic  Only hadrons  K- „ v  A —» n p  Now we turn specifically to muon capture and the leptonic part of the weak current. The muonic current has V - A structure and is given by[ ]: 23  •'l= lV,(lt/<H l  where js =  Y1Y2Y3Y4,  •  (1-20)  is the neutrino field, 4^ is the muon field, and y>. are the Dirac  matrices. Since the weak interaction couples to only left handed particles and right handed antiparticles, this current in Equation 1.20 has the l+y form. This leptonic 5  current is well understood; in particular there is the concept of lepton universality which. states that the weak coupling constants are the same for e, p, T. Experimental verification has been obtained to the in T and Z decays. Specificaly, in T decays e/u and T/U.  universality has been tested'to the 0.25% level[ "], which confirms the 0.15% test for e/u 4  universality which comes for pion decay[ ]. 43  The hadronic current, on the other hand, is not as well understood, because the strong interaction induces extra structure. The V-A structure is still present; through the use of the Gell-Mann-Cabibbo[ , ] Universality Hypothesis, the muon capture hadronic 46 47  current can be written as:  (1.21)  ^y\)' - cos o ( [ / ' , - M ' , ) , (  where the vector and axial vector interactions are given by:  8.M 2M  SATA/5  QxYi  m  u  where a^  = v  i/2(yxy -ivYx), v  MN  (1.22)  m„  K  (1.23)  „, , 2M N  is the nucleon mass, and m is the lepton mass. The M  Cabibbo angle, 9c, was introduced to explain why the strengths of the strangeness changing and strangeness conserving weak interactions were not the same. The Cabibbo angle allowed the quark generations to mix. The Cabibbo angle.is used in a 2x2 matrix form, presently a 3x3 matrix form is used for the quark mixing. In the original 3x3 48  matrix form cos 6c is equivalent to V [ ]. The coupling constants, gj, in Equations 1.21 ud  and 1.22 depend on the momentum transferred, qx n\.- p>„ where n?, is the neutron =  momentum and p\ is the proton momentum. In the q -» 0 limit, only the vector (gy) and 2  22  axial vector (g ) coupling constants contribute to the hadronic current, p-decay occurs A  close to this q —> 0 limit. The other four coupling constants are induced by the strong interaction effects and are seen in muon capture because the momentum transferred can be quite large. The g coupling constant measures the strength of the induced weak M  magnetic (o?^) interaction. The gs coupling measures the strength of the induced scalar interaction(I). The gp coupling constant measures the strength of the induced pseudoscalar interaction (ys). Finally, the gr coupling constant is a measure of the tensor (o"xvys) interaction.  1.6 The Weak Coupling Constants There are. several theoretical constraints on weak muon capture coupling ' constants. Time reversal invariance (t —> -t) is one. Time reversal invariance conservation implies that all the couplings are real. Time reversal violation has been . found in the neutral kaon system at the level of 10~ , but that is negligible for the 3  considerations of this thesis. A second conservation symmetry is G-parity. G-parity is given by  C/  = Cexp(//T7;) ,  ,,  (1.24)  where C is the charge conjugation operator and T is an isospin operator. A n example of 2  the use of the G parity operator is:  23  G  (1,25)  Since the strong interaction is invariant under G.-parity, and the induced currents are due to the strong interaction, the coupling constants which do not conserve G-parity must be zero. The interactions corresponding to the coupling constants gs and gj do not conserve G-parity, so they are zero. Weinberg [ ] considered these two types of interactions, S 49  and T, "second class" interactions. Nonzero second class currents have been searched for by many experimenters, but so far only one group[ ] has claimed experimental evidence 30  for them. They found a nonzero tensor interaction in P-ray angular distributions in the A=12 system. This experimental result would.have to be confirmed; until then we will assume the tensor interaction is zero, experimentally. A neutral atom trap experiment at TRIUMF is in the process of searching for scalar interactions^ ]. The limits on these 1  types of interactions are not very tight. Second class currents have been reviewed by Grenacsf ]. 32  The Conserved Vector Current (CVC) hypothesis was postulated by Feynman and Gell-Mann [ ],but actually first given by Gershtein and Zeldovich[ ]. CVC states that 3j  54  the vector part of the weak current is conserved, just like the electric charge is conserved in the electromagnetic theory. CVC implies that the divergence of the vector current is zero:  s,v, =.o  (1.26)  24  CVC is contained within the Standard Model, and has been tested by many .experiments. The branching ratio of the pion beta decay (n —> n° e v ) is an excellent test of CVC and +  +  e  was measured at LAMPF by McFarlane et al. ["] to be 1.026(39) x 10" , whilst theory 8  o  based on CVC predicts it to be 1.048(5) x 10" . The best confirmation of CVC is through superallowed Fermi 0—>• 0 nuclear beta decays [ ]. +  +  ?6  The CVC hypothesis reinforces that g = 0.. At the low energy limit of q -» 0, it 2  s  implies that gv = 1.0, but there is a slight momentum dependence of gv, which implies for muon capture g (q = 0.88m,/) = 0.978. ' . 2  v  CVC predicted the g coupling constant. This coupling constant is called weak M  magnetism because it is related to the anomalous magnetic moments of the neutron and of the protori. In the limit q -» 0, g = 3.706 theoretically, but like gv', gM has a slight 2  M  momentum dependence. So again, for muon capture gM(q  2 =  theoretically.  0.88m ) = 3.591 2  M  ;  CVC also implies that the g and g coupling constants remain the same when a v  M  nucleon is embedded in the nucleus. The final restriction on the coupling constants comes from the Partially Conserved Axial Current hypothesis (PCAC). PCAC states that the weak hadronic axial current '(Ax) is conserved for massless pions. The pion has a small nonzero mass, therefore the hypothesis is only partially conserved which implies  5  A  fr»h<l>.  (1.27)  where f is the charged pion.decay constant and ^ is the pion field. Once applied PCAC n  implies  . . . "  2  M  „  g  ^  .  M  ^  ,  '  ,  ( l  8 )  .which is a relation between g and g . In this expression G^NN is the strong pion nucleon A  P  coupling constant. Taking the q  ^ VS7 =  where  = 1  '  3 2 ± 0  G^NN = 13.40 ± 0.8  '  0 limit, Goldberger and Trieman [ ] estimated  2  0 2  57  '  [ ] and f 58  n  <> L29  = 1 3 0 . 7 ± 0.1 ± 0 . 3 6  g is slightly different than the measured value of g = A  A  [ ] were used. This value for 59  1.2670 ± 0 . 0 0 2 8  [ ], which 59  comes from beta decay of the neutron. This is the Goldberger-Treiman discrepancy 60j  A  s s u m  lepton universality to be true in semi-leptonic interactions, this relation  j g n  applies to the muon interactions as well. Equation 1.28 above can be used to predict g . P  as follows:.  2M m N  As one can see g is a strong function of q and is dominated by the pion pole, which 2  P  implies that g is primarily due to single pion exchange (see Figure 1.3). For muon p  26  '  2  r>  61  capture on a proton gp(q~ = 0.88m ) = 8.9. A more recent calculation [ ] shows g p at tl  this q to be 8.44 ± 0.23. Both g p and g change when the nucleon is in the nucleus; due 2  A  to .nuclear structure effects. ; • , ' An experiment at TRIUMF looking at radiative muon capture (u~p ->  y n) has  measured a value for g p 1.5 times larger than predicted[ ]. The value for g p was V 62  extracted using a calculation by Fearing[ ]. This is a puzzle because ordinary muon 63  capture agrees with theory. Cheon and Cheounf ] recently proposed a solution to this 64  puzzle, but Fearing[ ] has cast doubt on this solution. 65  Table 1.7 gives the calculated and experimental predictions of the coupling constants, and the experimental techniques used. Table 1.7:. The values of the coupling constants. Coupling constant Theory Experiment 1.0 gv • 0.9755 ±0.0005 [ 1 3.706 gM 3.582 ±0.003 [ T 0 gs 0.001 ±0.008 [ Y 1.32 •. gA 1.238 ± 0.003 8.44 gP 8.7 ± 1.9 r ] 0 gT ' -0.06 ± 0.49[ , °1 66  66  6  68  69 7  Experimental Technique u decay p decay, u capture P decay Neutron P decay u, capture in H p decay, A - 1 2 '  FIGURE 1.3: THE PSEUDOSCALAR MUON CAPTURE REACTION.  It is hard to confirm these constants in muon capture for the case of the free proton. The best test is the recent measurement of muon capture,in He to the tritium 3  27  ground state, which has been measured to be 1496 ± 4 s'[ ]. Two recent calculations^ ] 71  2  obtain good agreement using the coupling constants given in Table 1.7. However at the recent conference on Mesons and Light Nuclei in Prague-Pruhonice, M. Oelsner of Hannover, working with E. Truhlik, reported a third calculation which left a 5% shortfall. This is a traditional problem of the Impulse Approximation approach, so we consider muon capture on .''He to be the best confirmation of our theoretical understanding, but we accept that something may be missing. Govaertsf ] recently wrote a review of present 66  status and future prospects of these coupling constants.  1.7 Allowed Muon Capture Transitions in N 14  One experiment performed in this thesis measured nuclear transitions in muon capture in N , including allowed transitions. Allowed transitions satisfy the following l4  Fermi and Gamow-Teller selection rules for nuclear spin and isospin quantum numbers:  Fermi: •  Gamow-Teller:  |J — JH = 0  |j — jrf s  ' n n =+l {  |Tj-Tf| = 0,l  n'n=+\  |T — Tf| = 0,1  x  S  .  ;  (no 0 -> 0)  where the subscripts (or superscripts) i stands for initial state and f stands for final state, n is the parity of the state in question, J is the angular momentum, and T is the isospin. Allowed transitions in A < 16 nuclei usually involve well known states, which implies  28  that knowledge of these allowed transitions can provide a test of the weak interaction 23  Hamiltonian (Equation 1.18). Table 1.8 shows a calculation by Mukhopadyay[ ] giving the relative contributions of the various hadronic.weak form factors from two models for muon capture on N,(' N -> C ( 2 l :7.01 MeV)). In the table, A is the axial 14  4  l4  +  contribution, PS is the pseudoscalar contribution, and V M is a mixed vector and weak magnetism contribution. The agreement between the two models is good, but it turns out that the Fujii-Primakoff approximation breaks down completely in the case where the GT matrix element is small (for example N(u.,v .-) C . . )[ ]. 14  14  23  M  g s  Using, an impulse approximation and nuclear wave functions from the BME and POT versions of the Cohen-Kufath[ ] model Mukhopadhyayf ] has calculated the muon 73  74  capture rates on N to the allowed transitions in C . The Cohen-Kurath shell model l 4  l4  describes all nuclei from mass A=6 to A=16 in the p shell with an effective interaction that was fitted to the energy levels of nuclei in that region (15 matrix elements and 2 single particle energies). These Cohen-Kurath wave functions are very successful when used to calculate other observables like magnetic moments, quadrupole moments, y-ray transition rates, and average p decay rates. This Cohen-Kurath model assumes an inert a core and 10 active nucleons which can populate the  \pm and  lp3/2  valence orbits.  In his calculation of the partial muon capture rates, Mukhopadhyay approximated the radial component of the nuclear wave functions to be those of a harmonic oscillator. He also ignored any effect from hyperfine transitions; this may have been an oversimplification, since a hyperfine effect has been measured for nitrogen (Section 2.3). These partial muon capture rates can be converted into, yields by dividing by the total capture rate measured by Suzuki[ ] (6.93 x 10 s" ). Table 1.9 has the yields in 19  4  1  29  percent. The table also contains an estimate For the same transitions if "conjectured" (2s - Id) mixed states are taken into account. Mukhopadhyay considered this 50% 2  .mixing of s p and s p (2s - Id) shell model representation to try to explain the factor 4  10  4  8  2  of two difference between his calculation and the only experimental result known at that time (the Dubna result discussed in Section 2.4). This may be a good approximation as this type of admixture is needed to explain the long lifetime of the beta decay of the C 14  ground state to the N ground statef ], but in this beta decay case the admixture was l 4  73  only a small percentage. Furthermore the calculated yield is about 28% of all muon capture in N . Common sense indicates that this is exceptionally high and unlikely to be 14  correct. One should then be cautious of such a large admixture and the fact that even the small admixture was not used in the original data fitting of Cohen and Kurath. As shown in the table, if this ground state mixing is correct then the muon partial capture rate to the second 2 state in C would be large. There is an 8.32 MeV 2 state in C. Capture to +  14  +  14  this state would lead to emission of a 150 keV neutron leaving C in the ground state. 13  Finding this missing strength would confirm this "conjectured" mixing. The model predicts a capture rate of approximately 1300 s" for the first 1 state, 1  +  at an energy of about 9 MeV. It turns out that in C there are two 9 MeV states l4  (9.746 MeV and 9.801 MeV) neither of which are 1 (0 and 3" respectively). The first 1 +  +  +  state is actually at 11.306 MeV [ ]. . 76  Table 1.8: The relative contributions in % of the various hadronic weak form factors from two models for muon capture on N ( N -> C(2 1:7.01 MeV) p ]. Model PS VM •A A-PS A-VM PS-VM "exact" 84.9 2.77. 2.35 -14.8 25.1 -0.18 Fujii-Primakoff 3.77 92.6 2.34 -22.3 23.6 0 14  14  14  +  23  30  Table 1.9: Muon Capture yields and partial capture rates to allowed transitions in C | ] (Total capture rate is 6.93 x 10 s~'). l 4  74  4  Energy Daughter BME Model (keV) State Partial . Capture Yield/ rate (s"') Capture 0.0C(0I), . 186 (%) 0.27 4 l  •' 6589:4 7012 8317.9 11306  +  POT Model " , , BME with (2s-ld) . POT with (2s-ld) Partial Partial „ Partial Yi e l d / Capture Capture Yield/ • Capture Yield/ rate (s) Capture rate (s') Capture rate (s) Capture (%) (%) 219 (%) 0.32 2  _l  1  C(01), 282 .0.41 • 114 0.16 C(2l), 1.98 x 10 28.57 1.96 x 10 ' 28.28 C(21) 0.64 9.24 x IO" 1.42 2.05 x 10" C(1 1), 1.20 x 10 / 1 73• 1.51 x 10 2.18  4 I  4 l  2  1 -  +  +  4 ,  +  14  +  4  4  4  2  3  J  J  9520 13.74 '9421 13.59. Rate«10 Yield •« 14 1 '1 1 4  1.8 Goals of The Experiments As will be seen in Chapter 2, a chemical effect in the muonic hyperfine transition rate may have been observed in Na and NaF. The goal of this thesis was to find more information on this possible chemical effect. Since the pseudoscalar coupling constant gp can be determined by measuring y-rays after muon capture in elements with nonzero spin, and since the ease of determining the coupling constant is strongly dependent on the hyperfine transition rate, the dream was to use the chemical effects to better determine gp in future experiments. The first observation of the chemical effect in the muonic hyperfine transition rate i n N a was-in an experiment using high purity Ge detectors. In this thesis, we used the technique of measuring with liquid scintillators the time spectrum of neutrons which are produced after muon capture. Unlike the source of y-rays, the source of the neutrons can not be determined from their energy spectrum, so instead of using Na and NaF, N a (metal) and N a H (nonmetal) were used. The idea is that the electrons in the nonmetal may not refill the atom as quickly after the muon cascade described in Section 1.2. The hydrogen present in the N a H does not affect the transition  /  rate, as any muons captured on the hydrogen are quickly transferred to the sodium. The time scale of this transfer is much less than a nanosecond. This time scale can be inferred from the pionic atom case, where pions, when stopped in hydrogenous materials, are mainly transfered to the heavy elements, yet the pionic atomic cascade time is (2.3 ± 0.6) 12  77  x 10" seconds] ].. Therefore the transfer of the pion is slightly shorter than this mean lifetimeof 10" seconds, so within 1 0 seconds the transfer from hydrogen to the 12  10  heavier element will be complete. This would be almost identical for the case of muons,, because both pion and muon are acting as heavy electrons during these interactions. By measuring the time spectra of neutrons, we made the experiment less limited by statistics than in the high purity Ge measurement, so other elements and compounds were also investigated. Of particular interest was N, because, as will be presented in Chapter 2, a hyperfine transition was observed in this element, whereas it should not have occurred. Along with the liquid scintillator technique of detecting neutrons after muon . capture, another experiment using high purity Ge detectors was also used to look for this hyperfine transition. Since the y-rays were detected, nuclear structure information was also obtained in the form of nuclear level yields. Chapter 2 of this thesis will describe previous muonic hyperfine transistion rate experiments and ancillary reactions (for nuclear structure), while Chapter 3 will describe the experiments of this thesis. Chapter 4 will describe how the data analysis was performed, the results of which will be looked at in Chapter 5. Chapter 6 will conclude the thesis.  ••  "  •32  Chapter 2: Previous Experiments 2.1 Previous Muonic Hyperfine Transition Rate Measurements using Liquid Scintillators As explained in Section 1.3, muon capture rates from different hyperfine levels differ a lot for odd Z nuclei. Using this difference, one can measure the hyperfine transition rate (AH) by measuring the time spectrum of the capture-products, namely emitted neutrons and y-rays. One method of measuring this time spectrum is. by the use of liquid scintillators. Previous to this work, there has only been one pioneering measurement of A H by the use of a liquid scintillatorf ]. That experiment was done at 26  the Chicago Synchrocyclotron, where Winston used plastic scintillators todefine a muon stop, a Lucite Cerenkov counter to reduce the electron beam contamination to 20%, and a 5" thick by 5" diameter liquid scintillator to.measure the neutral capture products (neutrons and y-rays). Winston used pulse shape discrimination to discriminate between y-ray and neutron events, and a plastic scintillator to reject decay electrons events. Using this method Winston measured the hyperfine transition rate for both y-rays and neutrons, and found the best evidence in fluorine, for which he used a LiF target. He also used LiOH and S as targets and saw no hyperfine effect in those two materials, as expected.  2.2 Previous Muonic Hyperfine Transition Rate Measurements using Germanium Detectors Hyperfine transition rates can also be determined by measuring the time spectra of y-rays via germanium (Ge) detectors. This method suffers from poor timing resolution and from low statistics, since only one nuclear transition is studied. The advantage of this method is that by measuring the difference between the nuclear capture rates (AA), one can get a measure of the pseudoscalar coupling constant in the nucleus under study without being particularly sensitive to the nuclear wavefunctions. 78  19  Recently, Gorringe et al.[ ] reported the measurement of hyperfine rates in F, 23  Na, and C l . The group also put a limit on the rate in P and found a possible nat  31  chemical dependence of the hyperfine transition rate in Na and NaF. The results of these measurements are presented in Table 2.1. The experiment was performed at TRIUMF. Plastic scintillators were used to define a muon stop, and a high purity Ge detector (20% efficiency relative to a 7.62 cm x 7.62 cm Nal) was used to measure the time spectra of individual y-ray transitions. A 10 fold segmented BGO detector surrounded the.Ge detector to suppress Compton scattering events. In a similar experiment Giffon et al.[ ] at the Saclay linac used a 100 cm coaxial 79  J  Ge(Li) detector to study the time dependence of the 7.01 MeV transition from muon capture in N and the 2.59 MeV transition from muon capture in B . By taking the ratio l4  l0  34  of the y-ray time spectra to the decay electron time spectra and putting it into four 1 us bins, Giffon et al. did not find a hyperfine transition for either of these elements. OA  J.P. Deutsch et al.[ ], at the CERN synchrocyclotron muon channel also used this 1  1  3  technique to measure the muonic hyperfine transition rate of B. They used a 35 cm Ge(Li) detector to measure the time spectrum of a 320 keV y-ray which was produced from muon capture on ' B . 1  81  A PSI group, Wiaux et al. [ ] is also currently investigating muonic hyperfine effects in B, using a germanium detector (Wiaux is supervised by J.P. Deutsch at 11  Louvain). The preliminary results from Wiaux et al. are also presented in Table 2.1.  2.3 Previous Muonic Hyperfine Transition Rate Measurements using Muon Spin Rotation (ju'SR) The only effective way to measure the hyperfine transition rate in even Z nuclei is by the use of u~SR, because in nuclei with an odd neutron there is little difference in the muon capture rates from the two hyperfine states. The idea behind the u'SR technique is to observe the depolarization of the muon when it makes the hyperfine transition. This method can also be used for odd Z nuclei, of course. Other mechanisms like fluctuations in the magnetic field can also give rise to a depolarization of the muon, so there can be systematic corrections. The specific technique is to apply a magnetic field to the muonic , atom to precess the muons in their orbits. When the muon decays, the decay electrons are emitted preferentially in the direction of the muon spin. If there is no hyperfine transition  35  and one observes the time spectra of the decay electrons, one would see the combination of sinusoidal curves with the precession frequency of each F* state. If there is a hyperfine splitting, however, then one would not see a pure sinusodial curve, because some of the muons would make the hyperfine transition and thereafter would precess out of phase. The first u"SR experiment to confirm hyperfine transitions was by Winston[ ], in which he used a 110G field on UF&. He found that the ratio of UF6 to carbon asymmetry parameters implied a fast hyperfine transition. The first use of u"SR to measure A directly was performed by Favart et al.[ ] at 82  H  the CERN muon channel facility at the 600 MeV synchrocyclotron. Favart et al. measured.An for ' B , and put limits on it for ' L i and Be as shown in Table 2.1. They l 0  n  6  7  9  did this by observing the relaxation of the F states and by fitting the electron time +  spectrum to:  N(t) = Af(0)exp(-A/)[l + a" cos(a>~t + <p~) + a e x p ( - A / ) c o s ( « / + <z>)] (2.1) +  +  +  w  where A is the muon disappearance rate, and or, co*, cp* are the coefficient, frequency, and phase respectively. The magnetic field used for each target was 250Gfor Be;300G 9  for I.i and " l i ; and 600G for B . r,7  •  10  o-i  Using the TD-u/SR method Brewer[ ] has also measured the hyperfine transition rate in Al, as shown in Table 2.1. He measured the time spectra of forward, backward, upward, and downward going decay electrons to form the horizontal and vertical asymmetry time spectra. He then used these spectra to measure the residual polarization after the hyperfine transition and related it to the hyperfine transition rate. 36  The hyperfine transition rate in C and N were also measured to-be nonzero by l3  1 4  Ishida et al[ ] using the TF-u"SR technique, where the depolarization rate was 30  . measured. The interesting thing about the N result is that it should be zero, if the Auger l 4  mechanism is the only mechanism for hyperfine transitions.  Table 2.1: Previous measurements of muonic hyperfine transition rates. Nuclide Magnetic Method A H (us" ) Moment Theory Experiment He -2.12 Ion chamber 0.006 ± 0.008 [ 1 Li 1 0.82 u"SR < 0.02 H 'Li 3/2 3.26 < 0.02 | | u'SR Be 3/2" -1.18 < 0.05 | | LISR B 1.80 0.25 (^"SR 3 0.21 ±0.05 [ ] 1  3  7I  b  +  +  x :  y  S 2  1U  +  82  "B  3/2"  2.69  LI'SR  .0.25  Ge Ge 1/Z ' 0.70 1 0:40  C:  U  14  N  +  iy  F  1/2".  /3  Na  3/2  2.63 222 .  +  •  2 /  31  i3  Al P  5/2 ,l/2  3.64 1.13  Cl  3/2  0.82  +  +  +  LI'SR H"SR  Ge Liquid Scint. Ge Ge Ge '  0.33 ± 0.05 f } 0.26 ± 0.06 [ 1 0.25 ± 0.07 [ ] 0.178 ± 0.018 0.020 ±0.012 [ ] 0.076 ±0.033 [ 1 NULL [ ] . 2  LI"SR  84  80  0.053 0.0  30  30  /y  5.8  5.8 ± 0.8\ ] 26  4.9 ± 1.2 f l • • 8.4 ± 1.9 r ] 15.5 ± l . i 41 ± 9 | | > 50 | | 78  14  u"SR  41  Ge Scintillators Ge  58 8  t  •  78  X 3  7 8  A  D  »  A  H  \*T '  6.5 ± 0.9T l 78  * Preliminary Result ** A = l.l (.is"' :  D  37  2.4 Previous Measurements of ju N Partial Capture Rates 14  A l l previously measured partial capture rates of y-rays from muon capture of are of only one of the transitions in  l 4  l 4  N  C , namely the 7010 M e V transition. These results  are presented in Table 2.2. The first measurement of this partial capture rate was performed by a Dubna 88  group [ ], where they used N a l detectors (which have a much poorer energy resolution than Ge detectors). A Louvain group[ ] working at C E R N has also measured the partial capture rate using a G e ( L i ) detector. A PSI group[ ] (the lab formally known as SIN) had also measured the partial 90  capture rate by stopping muons in lithium amide powder (L1NH2). They measured the 7 M e V y-rays with a 95 c m coaxial G e ( L i ) detector and later on w i t h a 75 c m Ge(Li) 3  J  detector. The only published measurement was done by Giffon et al.[ ] at Saclay by 79  stopping muons in melamine (C3H6N6) with N b and Fe impurities. The resulting y-rays were measured with a 100 c m coaxial Ge(Li) detector. The partial capture rates were 3  measured by taking the ratio of y-rays to stopped muons. To avoid the hard measurement, of the number of muon stops, Giffon et al. used the 2p —> Is muonic x-rays to count the number of muon stops. In the case of  1 4  N , where the energies of the x-ray (* 0.1 M e V )  and the y-ray (« 7 M e V ) are different by two orders of magnitude, calibrated impurities (Nb and Fe) were used to correct for the energy dependance of the efficiency of the  38  detector. Atomic capture ratios are, however, not independent of the chemical environment, so there were probably unknown systematic errors in their yield estimates.  Table 2.2: The previous measurements of partial muon capture rates in N to the 7010 keV level. • , • . Experiment Partial capture rate (s" ) Yield/muon capture (%) Saclay[ ] 4640 ±700 6.7 ± 1.0 Dubna[ ] 10000 ±3000 14.4 ±4.3 Louvainf ] 8000 11.5 . . .. PSI(SIN)[ ] 6000 ±1500 8.7 ± 2 . 2 . l4  1  /y  8S  89  yu  2.5 Ancillary Reactions Different nuclear reactions complement and support each other when it pertains to nuclear structure. Muon capture reactions do not give us directly the energies of the excited states of the residual nuclei as the observed y-rays are often part of a cascade. Thus some prior knowledge of nuclear transitions is needed. The following reactions: 2  *  2  (n,p), (n,y), and (d, He) give us the excited states directly, because p, y, and He are easily detectable unlike v. These three types of reactions are very similar to (u,v) • because they all excite 1 transitions (among others), which are called Gamow-Teller +  (GT) transitions. . Much of the muon capture reaction goes to fairly high excited states in the final nucleus ( C in our case of u~N). These can be ..giant dipole resonance states, or the 14  reaction can be described as a quasi-free reaction (p"p —> vn), where the neutron escapes without having formed a coherent state; this is frequently called the pole term, especially • in the (7i ,y) reaction, and it may be subtracted off before a spectrum is presented. The _  39  pole term effectively describes a knock-out reaction and is akin to (p,2p) and (e.e'p), or even the (y,p) reaction. It is interesting to know the relative feeding of the states in the final nucleus ( C in our case of LTN). lj  Specifically, the N(7i",y) C reactionf ] was measured at PSI.using stopped n. 14  14  91  The photons were detected by a pair spectrometer with a resolution of about 1 MeV, so itcould not separate the known levels of C . Figure 2.1 shoWs that photon energy l4  spectrum, along with the observed states in C, and with the C binding thresholds. 14  13  These states are shown in Table 2.3 along with their absolute branching ratio per'stopped TT. Even though the pion is absorbed in the 2p state as well as the 1 s state, the reaction rates are often similar. Figure 2.1 has had the pole term subtracted out. Figure 2.2 shows the same type of experiment performed by Baer et al.f ] without the pole term subtracted 92  out.  It is clear that Mukhopadyay's calculation for muonic capture in N to the 7.01 14  MeV state is unrealistic. In the case of N(n,p) C, 60 MeV neutrons were used at the Crocker Nuclear 14  14  Laboratory. The strongest transitions seen were to C*(7.0+8.3, 11.3, 15.4 MeV) and to 14  a giant resonance peak at -20.4 MeV. Another reaction which supplements muon capture is the (y,p) reaction. Gellie et al. f ] was studying the photoneutron, N(y,n), cross sections and found that some of the 93  14  neutrons they observed came from N(y,p) C type reactions. So to estimate this 14  13  contribution, Gellie et al., reviewed the N(y,p) C partial cross sections in a table which 14  13  is presented here as Table 2.4. The conclusion of Gellie et al., was that the photdisintegration of N is well represented by a shell model description where single 14  nucleons are promoted from the p shell. They also found that there was a close  40  agreement between photoproton and photoneutron transition strengths, which imply a high degree of isospin purity for the giant dipole state. A reaction similar to N(Lf,vh)' C is N(p,2p) C. These two reactions are l4  J  l4  13  almost identical in the strengths of the levels that they tend to excite in C , except in the lj  case of muon capture experiments the ground state of C will not be seen because the l3  neutrino cannot be detected. So the N(p,2p) C reaction to the C ground state can l4  l3  l 3  give an estimate of how often muon capture feeds the C ground state. Welch et al.f ], l j  94  performed the N(p,2p) C experiment at the 46 MeV sector focused cyclotron at 14  13  University of California in Los Angeles. They bombarded N with 46 MeV protons. 14  The two outgoing protons were measured by counter telescopes, which consisted of an • -energy loss (AE) counter which was a 250 (am surface barrier silicon detector and consisted of a total energy (E) detector which was a combination of a 2mm surface barrier silicon detector and of a 3 mm.Si(Li) detector. Figure 2.3 shows the summed energy spectrum of both of the outgoing protons each at 50°. The energy threshold of each proton detector was set at 5:5 MeV, which is the reason for the low energy cut off. The experiment obtained an energy resolution of about 1.5 MeV, so it does not resolve the three bound excitations in C, unlike the work of this thesis. It does show however 13  two unbound excitations and the . C ground state. A related reaction is N(p,d)' N which has also been studied extensively.. Since 14  13 , J  3  13  N and ' X are mirror nuclei (as shown in Figure 2.4), the reaction mechanisms are  similar and the neutron pick up shows a similar pattern as seen in Figure 2.5. This figure shows the results of a N(p,d) N experiment at 65 MeV performed by Roos et al.f ]. 14  l3  95  The experiment was performed at the University of Maryland Cyclotron, with a beam  current of 200 nA. The detector telescope consisted of a 1 mm Si surface barrier AE detector and a 4 mm Si(Li) E detector. The energy resolution of the system was between 150 keV and 300 keV (FWHM). It is interesting that there.is no evidence for the 2.36 MeV level in N 1 J  (3.089  MeV level in C), whereas an experiment at lower energies 1J  (18.5 MeV) by E.F. Bennettf ], has seen this 2.36 MeV level. This level should not be 96  seen in neutron pick up reactions if the  l 4  N ground state has a pure p configuration, 10  because then the reaction involves an orbital change for two particles (p —> p s). If the 10  l 4  8  N is not pure p and has a small p s or p sd configuration, then one will find some 10  8  2  8  pick up reactions to the Nfirstexcited state through p s —> p s or p sd -» p s i 3  8  2  8  8  8  transitionsf , ]. These are the same configuration mixings that are discussed in Section 97 98  1.7. This level is also seen in the muon capture reaction as will be shown in Section 5.4. In the case of muon capture the reaction is more complicated and would need a detailed calculation. Confirmation of this general picture comes from experiments which measured the ". number of neutrons per captured muonf , ]. Typically 30% of the time there are no 99  100  neutrons emitted, 50% of the time there is one neutron emitted, and 20% of the time two or more neutrons are emitted.. In light elements there is much variation and unfortunately no data appear to exist for muon capture in nitrogen. Table 2.3: The transitions seen from' N(7i-,y) C [ ]. Energy (MeV) Absolute branching ratio/stopped n (%) 4  r o  +  0.0 6.73  o  +  6.90  2  +  7.01  2  +  8.32  3.37 + 0.34  10.7  2.34 + 0.38  1  91  0.25 ± 0 . 1 1  ->+  +  14  6.22 +.0.40  42  14>  C level (MeV) Ground state 3.68 7.55 8.66  ,13,  Cross section (MeV-mb) 20 6.5 17 Visible but not separate from other reactions Visible but not separate from other reactions  IJ  9.52 11.80  5*. • . The transition strength maybe substantially higher, because the measurement only measured the part which yields 6.3 M e V neutrons via the C ground state. l 3  150  2 2 3" +  Pl  100  50 3  14  N(7C7Y) C 14  hy  C(V) n\; +  3, 3  0  +  C(g.s)+n--- ^-__  120  N  ExC C) 4  125  130 135 Photon Energy (MeV)  FIGURE 2.1: THE ENERGY SPECTRUM OF' N(7I",Y)' C [ ] WITH THE POLE TERM SUBTRACTED. 4  4  91  140  FIGURE 2.2: THE ENERGY SPECTRUM OF N ( 7 i ; y ) C [ ] WITH THE POLE TERM AND A RESONANCE IN C . A T • 20 M E V AS INDICATED. . . H  , 4  i  92  I  I4  I  I  MeV FIGURE 2.3: THE ENERGY SPECTRUM OF N ( P , 2 P ) C [ ]. H  13  94  44  -7/r  14.05  3/21 •  3.55 3.50^ 2.36  5/2*1  '13 OBS  WW  7/7  H0.75=  =7/7:  9.90  3/7  8.86  1/7  .7.55:yyyyyyyyyyyyy-  3.85  -3/2^4  13  c  4.94635. 12, C+ri  1/21  [+0.06] 1/2"  13  +  N  1/2"  FIGURE 2.4: THE PARTIAL ISOBARIC. DIAGRAM FOR A =13 (ENERGY IN M E V ) .  E FIGURE 2.5: THE ENERGY SPECTRUM OF N ( P , D ) N 14  I3  e x  [ ]. 95  (MeV)  Chapter 3: Description of Experiments The experiments were performed on the M9B channel at the TRI-University Meson Facility (TRIUMF), Vancouver, Canada. There were three experiments performed on the following dates: November 1994, August 1995, and May 1996. The primary purpose of these experiments was to measure the muonic hyperfine transition rate in various targets, namely, (CF) , LiF, NaH, Na, LiAlH , Al, P (in November 1994), n  4  and liquid nitrogen (in August 1995 and May 1996). The technique used for both the November 1994 experiment and the August 1995 experiment was to measure the time spectra of neutrons following muon capture by the use of liquid plastic scintillators. For the May 1996 experiment, the time spectra of y-rays were measured via high purity germanium (HPGe) detectors. The time spectra in both of these methods can yield the muon hyperfine transition rate. In the May 1996 experiment, some secondary information was also obtained on the yields of y-rays produced by muon capture.  3.1 Muon Beam production At TRIUMF negatively charged hydrogen ions are accelerated in a cyclotron. Then, to select an energy of these ions, a carbon foil is.placed appropriately in the path of these ions. The result is a proton, which has had the two electrons stripped off, travelling in an oppositely curved path out of the cyclotron and down a beamline. This stripping  46  can be done in various places aroundthe cyclotron. Figure 3.1 shows the layout of TRIUMF's'beamlines. One beamline, namely beamline 2A(p) is currently being commissioned. On April 29, 1998, the first beam in this beamline was extracted at an energy of 492 MeV. This beam will be used in the future for the IS AC (Isotope Separator and Accelerator) facility. Currently there are 3 beamlines which are operational and used for experiments. Beamline 4(p) is used for proton experiments. Beamline 2C(p) is used for the proton therapy treatment of cancer of the eye (choroidal melanomas specifically). Beamline l(p) is used to produce pions, which can be used for experiments in short channels. If these pions are used in longer channels (i.e. allowed to decay), their products, namely muons, can be contained arid used in experiments, Note that surface muons can also be used on the shorter channels. These operational beamlines can have proton beam currents up to 140 uA, with energies between 183 and 520 MeV. This beam is delivered in 3 ns pulses every 43 ns for a 99% duty factor, corresponding to the RF accelerating voltage.  47  FIGURE 3.1: THE T R I U M F BEAMLINES.  48  For muon production on the M9B channel, the proton beam strikes the T2 target as shown in Figure 3:1. This target is typically a water cooled piece of Be, 100 mm thick along the beam axis, 5 mm wide and 15 mm tall. Once the beam hits the target, pions are produced and go down the M9B channel, which is shown in more detail in Figure 3.2. The pions go through focusing and bending magnets until they reach the superconducting solenoid. In the solenoid pions decay in flight to muons and neutrinos: Then bending magnets and quadrupole magnets are used to select the momentum of the muons and focus them. By setting this last bending magnet to a momentum optimized for muons, the pions.are swept out of the. beam. The net result is a muon beam which has a pion contamination of <0.2% and a electron contamination of -20% [ ]l01  3.2 Beam Telescope arid Targets . Once the muons leave the last focusing magnet of the M9B channel, they go through a mylar window, out of vacuum, and into air. Then the muons pass through a collimator made of lead and polyethylene. The beam view and the side view of the collimator are shown in Figure 3.3. It is made out of lead bricks, which are surrounded by 1.27 cm (1/2") thick polyethylene. The polyethylene.surrounds the lead surfaces, which face the beam, thus the negative muons stop in carbon rather than lead. For muons stopping in carbon, very little nuclear muon capture occurs; Instead, the muons that hit the collimator will decay in orbit into electrons. The lead in the collimator is then used to stop these electrons and any other stray beam related particles. If the muons stop in the  50  lead, many more neutrons are produced and create a serious background for the experimental measurement. Figure 3.4 shows the telescope arrangement and the collimator. The beam telescope consists of 3 plastic scintillators, named SI, S2, and S3. Table 3.1 lists the sizes of these scintillators for each experimental setup.  FIGURE 3.3: T H E COLLIMATOR.  FIGURE 3.4: T H E BEAM TELESCOPE: COLLIMATOR (BLACK A N D G R E Y ) ; SCINTILLATORS S I , S2, S3 (IN ORANGE); TARGET (YELLOW); A N D M U - M E T A L SHIELD (BLACK CYLINDER).  51  Table 3.1: Sizes of beam telescope scintillators (cm) Experiment November 1994 August 1995 Detector SI 13.34x 13.34x 0.32 .13.34 x 13.34x 0.32 S2. 5.08 <j)x 0.16 5.08 <j)x 0.16 S3 15.24x20.32x0.32 20.32 x 20.32x0.32  March 1996 19.69 x 13.97x 0.32 5.08 (]> x 0.16 20.32 x 20.32 x 0.32  The muons pass through S1 just after the collimator. Then they hit the beam defining counter, S2, before entering the target. If they pass through the target they leave some energy in S3. Hence a muon stop is defined as a hit in SI and S2, but not in S3. The targets used in the 3 experimental setups are listed in Table 3.2. In the case of the liquid nitrogen target, it was simply a styrofoam container, which had to be filled every 10 hours. Styrofoam is a polystyrene plastic expanded into a nonpermeable multicellular mass approximately 42 times the original size. The muon entry side of the *  2  styrofoam container was 2.2 cm (66 mg/cm ) thick. It is composed of only carbon and hydrogen. Each target was surrounded by a 7.05 cm radius by 13.9 cm long hollow cylindrical mu-metal shield. In the case of liquid nitrogen the shield was immersed in the liquid nitrogen. The shield reduced the stray magnetic field from 1.5 gauss to 0.1 gauss at the target location. This was to reduce the stray magnetic field's effect on the muon magnetic moment, which can precess and affect the measured muon lifetime. In the case of the neutron detection experiments, these precession effects were further minimized by the placement of the four detectors as described in Section 3.3 and by adding the time spectra of individual detectors together. Since the detectors were placed upstream and downstream of the target, depolarization effects were also, avoided. In the cases when the  52  target was thin, 6 pieces of plastic degrader were inserted into the beam, right after the collimator. This degrader increased the number of muon stops in the target material.  Table 3.2: List of targets used. Target (CF) ; . LiF (powder) NaH (powder) Na LiAlFLi (powder) Al . Red P (powder) LiCl CC1 K Liquid N2 n  4  Size (cm) 10.3 cj) x 2.0 9.4 (h x 5.1 9.4 <> ( x 2.4 9.4 <b x 2.0 9.4<|>x3.0 9.4 <> ) x 3.0 9.4 <b x 2.6 9.4 (b x 2.5 •9.4(|)x4.0  9.4 <bx 2.5. 21.5 (beam) x 19.5 (wide) x 55 (tall)  Experiment Nov 1994 Nov 1994 Nov 1994 Nov 1994 Nov 1994 Nov 1994 Nov J994 Nov 1994 Nov 1994 Nov 1994 Aug 1995 May 1996  3.3 Neutron Experimental Setup As shown in Figure 3.5, four cylindrical liquid scintillators were used in the neutron experiments. Namely, NI and N2 were 12.7 cm diameter by 10.16 cm long (5". diameter by 4" long) NE213 liquid scintillators. N3 was a 12.7 cm diameter by 5.08 cm long (5" diameter by-2" long) NE224 liquid scintillator. N4 was a 12.7 cm diameter by 12.7 cm long (5" diameter by 5"long) BC501A (note: BC501A is equivalent to NE213) liquid scintillator. These detectors were at 45°, 135°, 225°, and 315° angles with respect  to the muon beam. Each detector has a time resolution less than 5 ns full width halfmaximum for y-rays. All four of these detectors can discriminate between neutrons and gamma rays via pulse shape discrimination. Pulse shape discrimination works on the principle that neutrons and y-rays interact in the scintillator in different ways. Gamma rays interact through photoelectric, Compton, and pair production processes. Neutrons, on the other hand, scatter protons in the liquid scintillator, which lose energy with a different dE/dx (energy loss over path length) than the y-rays. These different energy loss mechanisms tend to populate different states in the liquid scintillator in different proportions. These states have slow and fast components of de-excitation, so the relative intensities of the slow and fast components are different for different dE/dx. This fact implies that the shape of the light pulse will be different for particles which have different dE/dx. By measuring the light output in a certain way (as discussed in Section 3.6), one can discriminate between neutrons and y-rays. In order for the apparatus to discriminate against charged particles, 8" x 8" x 1/8" plastic scintillators were placed in front of each liquid scintillator. These plastic scintillators were labeled C l , C2, C3, and C4.  54  FIGURE 3.5: T H E NEUTRON EXPERIMENTAL SETUP: NI A N D N 2 (GREEN); N3 (ORANGE); N4 (YELLOW); C l , C2, C3, C4, (BLUE); A N D THE BEAM TELESCOPE FROM FIGURE 3.4.  3A The Gamma Ray Experimental Setup Figure 3.6 shows the gamma ray experimental apparatus. Two high purity germanium detectors (HPGe) were used. These detectors, Gel and Ge2, were 44% and 21% relative efficiency (with respect to a 7.62 cm diameter by 7.62 long Nal(Tl) detector). Each had a system energy resolution at 1.3 MeV of 2.53 keV and 2.19 keV respectively. Their timing resolutions at 1.3 MeV were 6 ns and 7 ns respectively (as measured with respect to one of the segments in their corresponding Compton suppressors). These Ge detectors were at 90° with respect to the beam direction. Their front windows were 27.5 cm and 33.1 cm awayfromthe center of the target respectively. Each of the two Ge detectors had a plastic scintillator infrontof them, to eliminate the backgroundfrommuon decay electrons. These detectors were named El and E2.  55  The two Ge detectors were surrounded by Compton suppressors named CSA and CSB. Each suppressor was a segmented array of Nal(Tl) crystals. These crystals were arranged in a coaxial geometry. The purpose of this Nal(Tl) annulus was to detect gamma rays which had struck the Ge detector and scattered out of it, and hence did not leave all of their energy in the crystal. This type of event is not always useful, so the annuli were operated in anticoincidence mode in software. By using the Compton suppressor in this mode, the peak signal to noise is greatly improved (by approximately a factor of 5) allowing low intensity y-rays to be seen. This improvement is especially useful when the Ge detector observes many y-rays and neutrons.  FIGURE 3.6: T H E G E EXPERIMENTAL SETUP: G E I A N D G E 2 (LIGHT GREEN), C S A A N D C S B (GREY CYLINDERS), El A N D E 2 (BLUE), A N D THE BEAM TELESCOPE FROM FIGURE 3.4.  56  3.5 Beam Telescope Electronics • . ' , Figure 3.7 shows a, schematic of the beam telescope logic for the November 1994, and the August 1995 experiments, whereas Figure 3.8 shows the telescope logic for the May 1996-run. In these diagrams, V.S. stands for visual scaler, which is simply a logic pulse counting device, which is a useful online diagnostic. On the other hand, H.S. stands for hexscaler, which is a CAMAC module, which counts and records the number of logic pulses it receives. In all three experimental setups, the analog signals from the photomultiplier tubes on S l , S2, and S3 are sent into constant fraction discriminators (CFDs). The internal delay on these discriminators was set to 1 ns. These discriminators (Tennelec TC 455) produce a digital logic pulse for every input analog signal that is higher than a set threshold. If one looked at the analog signals for S l , S2 and S3, one Would see two bands. The lower band would correspond to electrons in the beam leaving some  57  Extra electronics for August run  FIGURE 3.7: ' T H E BEAM TELESCOPE LOGIC FOR THE NOVEMBER AND AUGUST EXPERIMENTS.  V-.S H.S Sl-  CFD  J  VS.  31-S2T S2-  S3-  CFD  1  V  H.S.  J |• VS.- H.S S1-S2-S3  J  t  Pile up Gate  CFD V.S. H.S.  7040 ns  UBC  >" B e a m condition"  10 ^is TDC A=0 , ,  U  A = 1  A = 2  Router I—|A=3 A=4  FIGURE 3.8: THE BEAM TELESCOPE LOGIC FOR THE M A Y EXPERIMENT.  energy in the scintillator. The upper band would correspond to muons leaving some energy in the scintillator. For S1 and S2, the discriminator threshold was set between the  58  two bands, so that only signals from the muons would result in a logic signal being produced. The S3 threshold was set just above the noise. The logic signals from SI and 52 were then sent to a coincidence unit, which defined the incident beam (51 • 52). The 53 logic signal was then put in anticoincidence.with 51 •52, thereby forming 51 • 52 • 53 (the bar above S3 indicates that a logic signal is not produced when S3 is in coincidence with 51 • 52. The 51 • 52 -53 logic pulses are an indication that the muon has stopped in the target. This 51 • 52 • 53 signal was then sent down two paths simultaneously. One path was to an updating pile up gate. This gate would be extended for a set amount of microseconds each time a signal was received. This gate was set at 9.2 us for the November experiment, 25 us for the August experiment, and 10 us for the May experiment. The output of this unit is the "beam condition", which is used in the strobe logic of Section 3.7. This beam condition is used so thatdata is recorded when there is a 51-52-53 signal or a stopped muon. The second path of the 51 • 52 • 53 signal is through various delays as shown in Figures 3.7 and 3.8. This signal is further split. One part would go to a UBC router box [  ]. The router box accepts a train of 4 logic pulses within a certain time window (5 and  10 us windows for the November experiment; 5,10, and 20 us windows for the August experiment; and 10.8 (is window for the May experiment) and then routes each of the 4 pulses out a separate output. Each of these outputs are sent to. four channels of a time to digital converter (modified LeCroy 2228 TDC), namely the A l , A2, A3, and A4 channels. Thus separate time spectra for each logic pulse, or in this case muon stop, would be.formed. These time spectra "also give, information on how many muons have  •  "  •  59  actually stopped in the target within the above set time. For example, if there were 2 muons that stopped in a target, and their time difference was 160 ns (well within the set time), then the first logic pulse would be sent to channel A l , and the second one would be sent to channel A2. The time difference of 160 ns would then be preserved within the two time spectra. The second part of the delayed 51 • S2 • S3 signal is sent directly to channel AO of the TDC. The histogram formed by this channel, would then be used as a check that the router explained above was working properly.  3.6 Neutron Detector Electronics Figure 3.9 shows a schematic for the N l and C l electronics logic for the November and August experiments. N2 and C2 are set up in the same way. The output of N l ' s photomultiplier tube (PMT) is sent to a pulse shape discriminator (PSD) electronics module. In this case the module is an Oxford Instruments TC 5020. This PSD module integrates the analog signal by the use of a short and long integration period. The output of either of these integrals is proportional to the energy the particle has left in the detector. The module has an output for this and it is labeled "energy" oh Figure 3.9. This digitized energy signal is sent through a linear fan in/fan out (FIFO) to an analog to digital converter (LeCroy 2259A ADC). Since neutrons have longer pulse tails than y-rays (see Figure 3.10) in the liquid scintillators that were used, the PSD unit can separate neutron and y-rays events by taking the difference:  PSD signal = L - aS ,  60  where L is the result of the long integrator, S is the result of the short integrator, and a is a variable amplification factor used to optimize the neutron and y-ray separation. The result of that last equation is the PSD signal, which is also sent through a FIFO to an A D C . This way a two dimensional histogram of energy vs. PSD can be used to discriminate between neutrons and y-rays in software.  Linear Nl-  TCJ020 PSD.  • Energy-  FIFO  •PSD —  Linear FIFO  ADC  —time—i n  V.S.H.S.  —n  1  640 ns  TRIUMF —| Pre scaler ~2  r  ^Strobe  Bit •. 1  i  D  1024 ns  Register  Dashed lines only in August 1995 run.  F I G U R E 3:9:  T H E ELECTRONICS FOR N 1 .  The PSD unit can also do the discrimination in hardware by setting an appropriate level. To be, safe, that level was set so that some y-ray events are identified as neutrons. Once that level is set properly, the unit will output logic signals for y-ray events (y) and neutron events (n). The T C 5020 PSD unit also has a built in constant fraction discriminator, which produces a "timing" signal. Finally, the unit also has a built in pile up protection circuit, so if there are two events within the long integration period, both events are rejected.  61  Since we are interested in neutron events, the y-ray logic signals are prescaled by a TRIUMF prescaler, set at 2 . That prescaled logic pulse is then "or"ed with the neutron 2  logic pulse. The "n or y" signal is then put in coincidence with the time output, so that the built'in constant fraction discriminator determines the timing (note that in the August experiment this built in discriminator was not working properly, so an external one was used for N2). That event signal is then delayed and sent to a C A M A C hex scaler (only for the August experiment) (H.S.), a visual scaler (V.S.), the "strobe" (which is described in the next section), and a bit register (a C A M A C device which is used to determine which counter has fired). . Figure 3.11 shows the set-up for N3, which is identical for N4. The only difference between this set-up and the one for N l is that a University of Alberta (UofA) PSD module is used instead of a TC 5020. The UofA module does not have a built in constant fraction discriminator or a built in pile up rejection circuit. So these functions were performed by external modules as shown in Figure 3.11.  62  Neutron/Gamma Pulse Shape Discrimination Amount of fast/slow decay components depends on dE/dx of the incident particle. Neutron Pulse Gamma Ray Pulse  Short Gate Long Gate FIGURE 3.10: PULSE SHAPE DISCRIMINATION FOR NEUTRONS AND Y-RAYS.  N3-  Linear FIFO  UofA PSD  -Energy-  Linear FIFO  -PSD—  Linear FIFO  ADC  1 CFD  •  Pile-up gate h-P400 ns  TRIUMF Prescaler  2  2  .  Delay generator 1/is C3—  Dashed lines only in August 1995 run  FIGURE 3.11: THE ELECTRONICS FOR N3.  V.S.H.S.  CFD  384 ns Gate 1 generator |  900 ns  Bit register  - Strobe  Both Figures 3.9 and 3.11 show the set-up of the electron scintillator electronics. This set-up is simply sending the PMT output to a constant fraction discriminator, then delaying the generated logic signal, and finally sending that signal to a bit register.  3.7 The Neutron Strobe Electronics Figure 3.12 shows the electronics for the neutron strobe. First the N l through N4 signals are timed together and then "or"ed together in a logic fan in/fan out. Then these signals are put in coincidence with the beam condition, so that only beam related events 16 Fold Register ->5tts T D C start  3>  "Beam Condition"  ^ • l O ^ s T D C start  V.S.  ->"20^s" T D C start  N l Strobe N2 Strobe N3 Strobe N4 Strobe—1  ->V.S. Gate Generator  4.8#s "Beam Condition"  " Strobe"  "Computer Busy" —J  H  1  2  8  n  s  Gate on Router Reset on Router  Gate Generator 10.3^s .  128 ns  Gate on Router Reset on Router  Gate Generator 20/ts  128 ns  Gate on Router Reset on Router  Inhibit-  Gate I—| Generator  Gate Generator 2#s Gate  Gate for T D C 5010 A D C Signals  D 100 ns Gate  Gate for U of A A D C Signals  NIM to NORMTTL  Starburst  Dashed lines only in August 1995 run.  FIGURE 3.12: THE NEUTRON STROBE ELECTRONICS DIAGRAM.  would be accepted. This coincidence was then vetoed by the inhibit signal. The result after this is a strobe logic signal. 64  The inhibit signal is produced to stop any other events from reaching the computer once the computer is already busy with an event. The inhibit signal is made up of three parts. The first part is the computer busy signal generated from a C A M A C module (Ortec ND027 NIM driver). This computer busy signal is generated about 120 ps after the strobe. An event within that 120 us would not be inhibited, so two more signals are added to the inhibit. The first is just the strobe signal itself from the fan out. But that is not enough to fill the gap, so agate generated 110 us pulse is also needed to fill in the 120 us gap. The strobe is then fanned out to: the gate for the 16 fold bit register, the start of the 5 us TDC, the 10 us TDC, the "20 us" TDC (only for the August Experiment), a visual scaler, three gate generators which supply gates and resets for three U B C routers (only 2 for the November experiment), gates for the ADCs for the energy and PSD signals, and finally a N I M to TTL level adapter which.goes to the starburst C A M A C module which starts the data acquisition. Note that the "20 ps" TDC is actually a 10 ps TDC, which is looking at time events between 10 ps and 20 ps after the muon has stopped.  ..  3.8 Germanium Experiment Detector Electronics Figure 3.13 shows the electronics logic for the detectors used in the y-ray experiment. The Gel signal was sent through a charge sensitive preamplifier to maximize its signal to noise ratio and to match impedances. This preamplifier has two  65  outputs, "energy" and "time". The energy signal was shaped, amplified, and the pole zero was adjusted by two spectroscopic amplifiers. The outputs of these two spectroscopic amplifiers (ORTEC 672 and ORTEC 973) were sent to two channels of a high speed, high resolution ORTEC AD413 A C A M A C ADC. One of these spectroscopic amplifier (ORTEC 672)/ADC combinations was set up for a low energy full-scale (-2 MeV). The other (ORTEC 973) was set up for a higher full-scale (-10 MeV). To reduce noise on the signals from the cables, this amplification and digitization was done in the experimental area, a few metres from the detectors. The timing output of the Gel preamplifier was sent to a timing filter amplifier (ORTEC 474). This timing filter amplifier shaped and amplified the signal. Two outputs of the amplifier were sent to two constant fraction discriminators (CFDs). One of the CFDs was set with a low threshold to set the timing. The second CFD was set with a high threshold to determine the energy threshold. This energy threshold was typically at -300 keV, but was lowered for some runs. These outputs of these two CFDs were then sent to a coincidence unit. This way the discriminators, timing dependence on the amplitude and the shape of the pulse was minimized. This coincidence signal was then put in coincidence with the beam condition from the telescope logic (see Section 3.5). The output of this beam related coincidence was then fed to a visual scaler, a hex scaler, and to another coincidence unit. At this next coincidence unit, the signal was vetoed if an inhibit signal was present (see Section 3.7). The output of this inhibited signal was then sent to a bit register and also became the "strobe". The electronics for Ge2 was setup similarly as shown in Figure 3.13, except a Tennelec TC243 spectroscopy amplifier was used instead of the ORTEC 973.  66  Figure 3.13 also shows the electronics schematic for one of the Compton suppressor segments, namely Compton suppressor A segment 1 (CS A1).. The CS A1 signal was split by a passive splitter, which sent part of the signal to an.ADC. The other part of the signal was sent to a discriminator. The output of this discriminator was then  In Experimental Area  Pre-amp  ~2 MeV Full Scale  - energy "time  -10 MeV Full Scale  ADC C h i ofAD431A  ADC Ch4 of AD431A  Ortec 973 spectroscopy amplifier  Ortec 672 spectroscopy amplifier  Timing Filter Amplifier  1 1  J  X  CFD High  Linear FIFO  CFD Low  V.S. H.S. to Strobe— Beam Condition-  256 Inlubit-  ~2 MeV Full Scale  In Experimental Area  - energyf re-amp  Passive Splitter  CSA1  -time  ADC C h 2 o f AD431A  TC 243 spectroscopy amplifier  Ortec 672 spectroscopy amplifier  -25%-  576. Jts_  ^75%-  i i i  fiS  Other C S A - | segments  El-  D  384 ns  CFD High  Linear FIFO  CFD Low  ADC 640  ™\  Bit Register  -10 MeV Full Scale  ADC Ch3ofAD431A  Timing Filter Amplifier  2  -Strobe  V.S. H.S. Beam Condition-  256 Inlubit-  71  2  £  6  -Strobe Bit Register  TDC  V.S.  —»Bit register 65 ns  —j TDC  E2-  D  288 ns  —*Bit register  . FIGURE 3.13: ELECTRONICS DIAGRAM FOR THE G E SETUP.  sent to a TDC stop and to a logic FIFO. This was done for all the segments of the Compton suppressor, but each segment had its discriminator output sent to the same logic FIFO. The output of this logic FIFO was then sent to a visual scaler for online  67  monitoring purposes. This setup was.also performed for Compton suppressor B (CSB). " The Compton suppressors were used in an offline, software mode. Figure 3T3 also shows the setup of the electron counters E l and E2. The signals from these counters were simply sent to a bit register and a TDC.  3.9 Germanium Experiment Strobe Electronics Figure 3.14 shows the electronics schematic for the germanium experiment strobe signal. This electronics setup is very similar to the one described in Section 3.7. The inhibit signal here is set up in the same way as in Section 3.7, but it is also sent to be in coincidence with a clock signal and the 51 • 52 • 53 signal for dead time measurements. This clock signal is generated by a 30 kHz pulse generator and is sent to an inhibited and uninhibited hex scaler. Similar to Section 3.7, the strobe is sent to: gate a 16 fold bit register, the start of two 500. ns TDCs, a visual scaler, start the starburst, a hex scaler, the gate generator for the gate and reset of a U B C router, the stop of a 10 ps TDC, gates for two ADCs, and to a gate generator which generates the gates for the high resolution ADC.  68  •V.S. •H.S. Gate for 16 fold register Start T D C 500 ns Start T D C 500 ns Stop T D C lOfis  TTLNorm ' Level adaptor  StarburstJll  Gate generator 14.84 (is TTLout :  10.82/zs  Gate for A D C 443A  64 ns  \ Gate for A D C I  64 ns  \ Gate for A D C I Gate of U B C Router  128 n s h — | Reset of U B C Router| NIM Output Register  101  (In Experimental Area)  pis  S1-S2-S3-T  FIFO  -^•Inhibit H.S.  Clock Pulse Generator 30 kHz  FIFO  H.S.  ->V.S. H.S.  FIGURE 3.14: THE STROBE ELECTRONICS FOR THE Y-RAY EXPERIMENT.  3.10 Data Acquisition The data acquisition was regulated by the TRIUMF VDACS system, which was made up of a V A X station 3200 and a PDP-11 front end processor (starburst). The V A X computer allowed experimenters to control data logging and online monitoring. It also uploaded the experimenter defined TWOTRAN program to the starburst. The starburst was responsible for the real time data acquisition from the CAMAC modules (TDCs, ADCs, bit registers, and hex scalers). The starburst was activated by the strobe signal, then the starburst called the TWOTRAN program, which then collected the relevant data from the C A M A C modules. This collected data was then written to 8 mm tapes for later analysis. The typical livetimes for the November and August neutron experiments were 0.90 and 0.96, respectively. For the germanium experiment, the livetimes can be found in Tables 4.9 and 4.10 under the L column.  70  Chapter 4: Analysis of the Data 4.1: How the Neutrons were separated from the Gamma Rays and Electrons For the liquid scintillator experiments (November and August), the method of pulse shape discrimination (PSD) was used to separate neutrons from y-rays and electrons. The electronics for this method are described in Section 3.6. To analyze the data, the University of Kentucky data analysis program DISPLAY was used to create a two dimensional histogram of the PSD vs. the energy signals from Section 3.6 for each liquid scintillator. This two dimensional histogram for the N l detector is shown in Figure 4.1. In this histogram one can easily see a "V". The left branch of the V is neutron events and the right branch is y-ray and electron events. This was determined by the use ofa Co source and an AmBe source. The Co source produces only y-rays, 60  60  whereas the AmBe source produces both neutrons and y-rays in approximately equal numbers per disintegration. The AmBe source makes setup easier than using a  Cf  2i2  source, because of these equal numbers. The y-ray events were separated from the electron events by reading the bit register which recorded events in the plastic scintillator in front of the neutron detector, as described in Section 3.6. If the electron bit registered as on, then it was an electron event, otherwise it was y-ray event. To select out the neutron events the two dimensional window shown in Figure 4.1 was used. If a prompt photon peak was seen in the neutron time spectrum, the bottom portion of two dimensional window was raised up.  71  o I"' ' '*&T ~" "i f  ;  •  0  ^_  20 '  ' (x) Signal Source No. 32  .—i •  ;  L  40, N2 y (PSD//) •  FIGURE 4.1: THE TWO DIMENSIONAL HISTOGRAM USED FOR NEUTRON DISCRIMINATION.  60 .  4.2 How the Hyperfine Transition Rates were obtained from the November Experiment The neutron time spectrum of a single detector was formed by making a histogram of the 5 us TDG data from Section 3.5. The conditions placed on this time spectrum were that:, the electron bit was off, the event must be within the neutron window described in the Section 4.1, only the detector of interest had fired, and there are no events in the router 2, 3, and 4 TDC spectra. The last condition was to avoid confusion about which muon caused the neutron event. This neutron time spectrum, was then converted from channels to time in ns, where the prompt x-ray peak in the raw time spectrum defined time zero. To measure the number of ns per channel, a time calibrator was used. Once each detector's time spectrum was in the form of time in ns vs. number of counts, the four time spectra were added together to form the time spectrum of the element or compound understudy. Before the hyperfine rate could be determined, some information was needed from some spin zero or non-hyperfine targets. To estimate time of flight effects of the neutrons, the non-hyperfine targets time spectra were fit to •) + ~Ve- +B Dl  J  ,  (4.1)  where D is the inverse lifetime of the target element, B is a constant describing the flat background, C is related to the number of events in the spectrum, and finally xo and s are parameters, used to model the time of flight effects. Table 4.1 shows s and xo values for various non-hyperfine elements.  Table 4 1: Values of s and x from nonhyperfine targets. z Target s (ns) xo(ns) At (ns)' £(MeV) 12. Mg 4.63 ±0.24 4.22 ±0.23 5.19 ±0.23 16.5 ± 1.6 14 Si 5.26 ±0.17 5.14 ± 0.17 6.11. ±0.17 11.9 ±0.7 16 S 4.84 ±0.12 4.35 ±0.14 5.32 ±0.14 15.7 ±0.9 29, Brass 5.92 ±0.11 9.72 ±0.11 10.69 ±0.11 3.9 + 0.1 30 (Cu+Zn) 79 Au 6.93 ±0.08 13.36 ±0.07 14.33 ±0.07 2.2 ±0.1 0  AE (MeV) 27 ± 4 20 ± 2 • 25 ± 2 14.9 ±0.7 10.4 ±0.3  Table 4.1 shows that s and xo tend to increase with the atomic number Z of each element. This can simply be interpreted that that for heavy elements the neutrons tend to be slower, and have a broader energy spectrum. This is a reasonable characteristic of evaporation neutrons. The column At includes the y-ray time of flight (0.97 ns) so is the time a neutron takes to go from the target to the counter. From this time difference one can calculate the average detected neutron energy, E . The parameter s is the standard 2  deviation of the range of neutron time of flight added in quadrature with the detector resolution. So s can be used to calculate the standard deviation of neutron energies (AE). In order to estimate s and xo for the hyperfine. elements, the two neighbouring spinless element values were averaged. For example, Al is between Si and Mg in the periodic Table, so its s value would be (4.63+5.26)/2 = 4.95. Table 4.2 shows the s and xo values for the hyperfine elements. For the case of Na, s and xo were taken as the Mg values. The hyperfine effect was much larger than the time of flight effects in the case of F, so in this case the s and XQ parameters were allowed to vary.  74  Table 4.2: Values of s and XQ for hyperfine elements. z  9  Element LiF (CF )„ Na Al P Cl K 2  11 13 15 17 19  s (ns) 5.38 ±0.17 (varied) 5.03 ±-0.13 (varied) 4.63 (fixed) 4.95 (fixed) 5.05 (fixed) 4.84 (fixed) 4.84 (fixed)  x (ns) 5.30 ±0.17 (varied) 5.19 ±0.28 (varied) 4:22 (fixed) 4.68 (fixed) 4.75 (fixed) 4.35 (fixed) 4.35 (fixed) 0  The amount of carbon background also had to be estimated before the time spectra could be fit. The percentage of muon stops in carbon was found by taking the ratio of SI • 52 and 51 • 52 • 53 results found from empty target runs. These ratios are 1.80 ± 0.25% of the muons stopped in carbon when the degrader was not used, and 4.47 ± 0.63%o of the muons stopped in the carbon if the degrader was used. In the case of potassium, 16% of the data were run in no degrader mode, so the last two mentioned ratios were weighted accordingly. These two ratios then had to be multiplied by 7%, because neutrons are only produced 7% of the time in muonic carbon atoms and divided by the percentage of the time that the muon was captured by the nucleus of interest. These values are shown in Table 4.3. The amplitude F of the carbon exponential was then calculated by  75  C(%carbon)(C ) • l ' - e " ' X  A  lifc  (4.2)  I  \-e  *  c  where C|jf is the muon lifetime in carbon, Xnf is the muon lifetime in the element o f e  e  interest, and t was set to 3500 ns (the amount o f time that was measured over). The percentage o f muon stops in carbon (%carbon) as determined above. W i t h all o f this information, the neutron time spectra for the hyperfine elements were fit to  erf(L ^-) T  "v2.y  + - {Ce-° (\-Ae- ")+:Fe^)+B 2J i  ,  t  (4.3)  where A is the asymmetry i n the capture rates, H is the hyperfine transition rate, and G is the inverse lifetime o f carbon. - For the compounds that had extra elements in them ( ( C F ) , L i F , and LiAlFLt), an 2  n  additional term is needed to describe the extra elements present: The ratio o f the number of muons which have stopped in each element, was estimated by the Z [  l03  ] , because insufficient data exists on this effect.  1 / j  approximation  So for example, for L i F , the ratio of  stopped muons is 1.44 for F : L i . These values could be incorrect by a significant amount (-30%). This ratio of muon stops was then multiplied by the ratio of the fractions o f times a neutron is produced for each element. These fractions were calculated using the capture rates[ ], and the decay rate o f the free muon. This resulted in the percentage o f 19  76  the time that neutrons were produced by the extra element. This result was then used to calculate P, the amplitude of the exponential decay of, the extra element. P was calculated as in Equation 4.2, where all the carbon parameter values were replaced by the appropriate values for the extra element in question (either Li or C). Table 4.3 lists all of the background correction values. Then once P was known, the time spectra of these elements ((CF )n, LiF, and LiAlH ) was then fit to 2  4  These fits were done using a % minimization, by the use of the MINUIT program. 2  The results of these fits are presented and discussed in Section 5.1. In the case of K, LiCl, and CCL, fitting in the above manner gave strange results. The value of the hyperfine rate, H, in these cases was of the order of 10" . A fast hyperfine effect was 8  apparent in the data, yet the data was of insufficient quality to uniquely define the parameters in the fitting function. The MINUIT program seemed to look for a slight correction to the lifetime in these materials, but lifetimes found without the hyperfine term were consistent with Suzukif ]. Using the lifetimes found with the MINUIT 19  program, the background corrections explained above, the time spectra data had the backgrounds subtracted, and were divided by e" . The data was also rebinned by 4. Dt  Then only the data between 20 ns and 1000 ns was preserved for fitting. This was to ignore the time of flight effects of the neutrons and to prevent the fitting program from looking for slight lifetime corrections. Then the data was fit to C(l-Ae~ ), using Ht  PLOTDATA. The values obtained for LiF from this method and the method using  equation 4.4 were consistent. The results of these fits described the data better in the cases of K, LiCl, CC1 . 4  Table 4.3: Background corrections Compound % carbon " (corrected for target nucleus) LiF (CF ) Na NaH Al LiAlH Red P LiCl CC1 K 2  4  n  4  0.376 • 9.8 0.278 0.695 0.207 0.518 0.436 0.402 1.97 0.358  for the hyperfine elements. % lithium Carbon (corrected for amplitude target nucleus) F (counts) 1.1 0 0 0 0 0.6 0 0.8 0 0  1.91 1.61 2.52 5.96 2.13 2.25 . 5.02 3.94 1.09 3.85  Extra. element amplitude P (counts) 16.7 40.16 0 0 0 4.27 0 7.82 11.62 0  4.3 How the Neutron Liquid Nitrogen Hyperfine Transition results were obtained. The analysis of the August experimental data, which used liquid nitrogen, was not performed in the same manner as in Section 4.2. If we believe the Ishida hyperfine transition rate measurement [ ] of 0.076 ± 0.033 us" (a time constant of 13.2 ±6.2 us), 30  1  then the hyperfine transition will affect the entire time spectrum. This hyperfine effect is unlike the ones of Section 4.2, which only affected the small time section of the spectrum. Figure 4.2 shows three neutron time spectra: no hyperfine transition present (A=0), the neutron time spectrum with the nuclear capture rate asymmetry measured by Ishida (A= -0.35), or the neutron time spectrum with maximal asymmetry (A=0.66).  78  10  3 \  Z5  O o  —  A=0 A=-035(jlSR result) A=0.66 (extreme)  10 0  FIGURE 4.2: POSSIBLE  5000  M  10000  Time; (ns)  N NEUTRON TIME SPECTRA.  15000  20000  .  As one can see the hyperfine effect simply results in what appears to be an overall change in the lifetime of the muon. Since the hyperfine effect on the electron time spectrum is usually much smaller than the hyperfine effect on the neutron time spectrum, then comparing the muon lifetime measured by electron and neutron detection should indicate if there is a hyperfine effect. In other words, if the lifetimes measured by electron and neutron detection were the same, then there would be no hyperfine effect. To do these comparisons, the neutron and electron time spectra were obtained in two fashions: the same way as in Section 4.2 (the single muon method) and by summing all four router spectra together instead of accepting only one muon events (the summed muon method). Instead of fitting the data to Equation 4.3, the time spectra werefitto  N(t) = Ce ' + Fe^'" + B D  (4.5)  where the carbon background was estimated the same way as in Section 4.2, except for the electron time spectra. The F values used in the electron time spectra were obtained by multiplying the empty target results by 93% and dividing by the percent of the time the muonic L N or muonic H 0 give off a decay electron. To provide a control, 2  2  measurements were also made on H 0 with u. and u" beams. The results of these fits are +  2  presented and discussed in Section 5.1.  4.4 Energy Calibration of Ge1 228  During the May experiment, sources (  152  Th and  Eu), muonic x-rays from I and  A u targets, and some background lines in the data were used to calibrate the energy spectra of G e l . The y-ray energy spectra were divided into three regions: 0 - 3 MeV, 2.6 - 5 MeV, and 5 - 9 MeV. The first region.is the entire output of the low energy full scale A D C of Section 3.8. The threshold in this region was above the u"N and the u"C xrays, so they could not be seen. The last two regions were parts of the high energy full scale A D C of Section 3.8. To convert from channels to energy the following linear calibration was use for each of the three regions:  Energy = m(channel + b) .  (4.6)  80  In the low energy region ( 0 - 3 MeV) the y-rays listed in Table 4.4 were used to calibrate the ADC. After fitting this data to Equation 4.6, m was found to be 0.35032 and b was found to be 4.6974. The medium energy region used the y-rays of Table 4.5 and the results of that fit were m = 5.0060 and b = 2.3628. Finally, in the high energy region the y-rays of Table 4.6 were used, which yielded rri = 5.0000 and b = 3.575. These calibrations were then used to identify the rest of the lines in the data for u." on liquid nitrogen. These identifications are presented in Section 5.2.  Table 4.4: The energies of the y-rays and x-rays used to calibrate the low energy region . of Gel. Source . Energy (keV) . ^ T h r i  l5i  Eu [ ] 104  u'Au x-rays  238.632(2) 583.191(2) 727.330(9) 860.564(5) 1620.735(10) 2614.533(10) 244.6989(10) 344.2811(19) 964.055(4) 1112.087(6) 1408.022(4) 400.143(50)  405.654(50) 869.98(12) 899.14(12) .2341.21(45) "T 105n 179.93(25) p 1 x-rays [ J 388.16(20) 394.30(18) 1150.42(15) r  81  Table 4.5: The energies of the y-rays and x-rays used to calibrate the medium energy region of Gel . •  Source Background from N(n,n' y) [ 1 l4  76  C line from muon capture [ 1 Th [ ] u"Au.x-rays [ l n ' u'l x-rays f ] U  2 2 8  IU6  l04  l05  107  Energy (keV) 5104.89 (10) 3853.170(2) 2614.533(10) 2341.21(45) 5591.71(15) 3667.361(35) 3723.742(35)  Table 4.6: The energies of the y-rays and x-rays used to calibrate the high energy region of Gel (the Fe(n,y) lines are background, but are useful for calibration). 56  Source -Fe(n,y) m Fe(n,y) [ ] Single escape of Fe(n,y) Single escape of Fe(n,y) Double escape of Fe(n,y) N(n;n' y) [ 1 u"Au x-rays [ ] i6  108 ,uy ;  36  36  36  14  76  107  Energy (keV) 7645.58(10) 7631.18(10) 7134.58(10) 7120.18(10) 6623.58(10) 5104.89(10) 5591.71(15)  82  4.5 How the y^ray Energy Peaks were Fit If the y-ray energy peak did not have enough statistics to be fit, then its centroid was estimated with the cursor. Otherwise if it was not Doppler broadened it was fit to a Gaussian and linear background:  y{x) = Ne2 [  S  + UAx + UB  (4.7)  where S is the width of the peak, E is the centroid, N is the amplitude, and UA and UB are background parameters. In the energy spectrum there were two neutrino Doppler broadened peaks (7010 keV, 6092 keV) and their single escape peaks. There was also one neutron Doppler broadened peak (3684 keV). The neutrino Doppler broadened peaks were fit to  • f ^  N  E(\-p)-x erf E(\ + j3)-x -erf. yf2S  V25  + UAx + UB ,  (4.8)  where E is the centroid of the peak, p is the recoil velocity of the nucleus divided by the speed of light (P = 0.00754 for the 6092 keV. y-ray and p = 0.00747 for the 7010 keV y-ray), S is a parameter dealing with the resolution of the Ge detector and with the lifetime of the nuclear excitation level, and N is the amplitude. The 7010 keV y-ray and its single escape peak were fit to Equation (4.8). The fit to this peak is shown in Figure 4.3 and is unusually clear of contamination.  83  • The 6092 keV y-ray had background peaks on it, so it was fit to Equation (4.8) summed with three separate Gaussian peaks (Equation 4.7). There were two background peaks on the 6092 keV y-ray, namely from Cl(n,y) at 6110.88 keV and 0 at : 35  16  6129.39 keV. The third peak was from a cascade from other levels in C . The widths of l4  these peaks were estimated and fixed. They were estimated by measuring the widths of other peaks shown in Table 4:7 and then interpolating. In this table there are two values for the Co lines, the first ones listed are for the case where a source was placed near the 60  detector while the beam was on, the second was simply from the background lines seen during regular data taking. The energies of these three Gaussian peaks were fixed. In the case of the cascade peak it was set to the centroid of the Doppler broadened peak. Figure 4.4 and Figure 4.5 shows two of these types of fits. This y-ray was fit in three different ways to model the systematic effects. In one case (Figure 4.4) the area of the Cl(n,y) 35  peak was estimated and fixed. The area of this peak was estimated from knowing the areas of other Cl(n,y) peaks, their branching ratios[ ], and the acceptance of the 35  I08  detector. In this case the background under the peak was allowed to be a straight line with nonzero slope. In the next case the area under the Cl(n,y) peak was allowed to 35  vary and the same background was assumed. This nonzero background does not seem to be correct, so in.the third model (Figure 4.5), the background was fixed to a flat line and the area under the Cl(n,y) peak was allowed to vary. By comparing these three models, 3:,  an estimate can be made of the systematic effects. The single escape peak of the 6092 keV peak (at 5581 keV), shown in Figure 4.6, had three background lines on it from I(n,y) at 5592.2 keV, Cl(n,y) at 5599.88, and i27  nat  84  I 6  0 at 5618.39.. These peaks were treated in the same way as above, except their areas  were not fixed, nor was there any evidence of a second Doppler broadened peak. The 3684 keV y-ray had a triangular shape, so it was fit to a straight line background, and a triangle shape which consisted'of two straight lines. The fit for this peak is shown in Figure 4.7. The results of these Doppler fits are discussed in Section 5.5.  2000 N S Be  .  EO  UA UB  1500  .2673330+03  + / -  .813970D+00  + / -  .1537600+00  + / -  .0000000+00  .7+70000-02 .1399780+04 -1.369007. .2Z1594D+0+  + / -  .7776720+01  .98212+D-01  + / + / -  0.2S20BS •393967D+03  S Q R T ( c h r 2 / d e g of f r e s )  la  1.9433  00  1000 o o  500 -  o— f6900  7000  710.0  Energy  FIGURE 4.3: THE 7010 K E V PEAK DOPPLER FIT  7200  (keV)  7300  1400 .905400D+02  1200 -  .2277350+02  .Z9S360D+03  +/.-  .OOOOOOD+00  .3I9881D+03  + / -  .2727780+02  §  o o  + / -  .OOOOOOD+00  .3532000+00  +/-  .OOOOOOD+00  + / -  .OOOOOOD+00  754O00D-02  + / -  .1214920+04  +/-  .1222300+04 -2.8-54500  •  38S965D+04  .OOOOOOD+00 210228D+00  + / -  ,OOO000D+OO  + / -  OOOOOOD+00  + / + / -  SQRTj(phi~2/dsg  600 H  .6864890+00  .8509000+00  .1Z1660D+0+  800  '  +./-  .655600D+00  V  .132210D+02  +/-  .1275250+01  1000 -  + / -  .1339670+03  0.619759 .7523850+03  of  fr< B) is  1.9627  400 200 6000  6100 .6200 Energy (keV)  6300  6400  FIGURE 4.4: ONE OF THE 3 DOPPLER FITS TO THE 6092' K E V PEAK.  1400 N  .1410370+03 N1  1200-  -  1000 H  .302314D+02  N2  .18250ZD+03  +/-  .240+92D+02  N3  .2954-72D+03  S  . 2 1 0 6 2 5 D+01  S1  .850900D+00  S2  .853200D+00  S3  .655600D+00  ZQ  800 H o o  UA UB  .656680D+01  +/,"  Be  V)  +/-  .68749BD+02  +/-  .276344D+02  +/+/+/-  .OOOOOOD+00  +/"  .553611D+00 .OOOOOOD+00 .OOOOOOD+00  .75+0000-02  +/-  •OOOOOOD+00  .121413D+04  +/"  .4434870+00  E2  .1Z1660D+0+  E3  .122230D+04 0.000000 .3970000+03  .+/-  +/-  +/-  +/-'  .OOOOOOD+00 OOOOOOD+00 0.000000 .OOOOOOD+00  SQRT£chi~2/dec. of fres) fa  600  1.9574  400 200 6000  6100 , 6200 Energy (keV)  6300 •  FIGURE 4.5: ANOTHER FIT TO THE 6092 K E V PEAK BUT WITH A FLAT BACKGROUND.  6400  .4-000. N N1 N2 N3 S SI S2 S3  '3500 -  Z5  Be E0 E2 E3  3000  o o  UA U8  .1769-37D+0J +/.553719D+02 .13601SD+03 +/.596823D+02 .1S6685D+03 +/.55+7290+02 .321441D+03 +/- -619769D+02 .163271D+01 +/.109007D+01 .786500D+00 +/.OOOOOOD+OO .783800D+00 +/OOOOOOD+OO -788900D+00 +/.OOOOOOD+00 .7540000-02 +/.OOOOOOD+OO .1112580+04 +/.346641D+00 .1TO627D+0+ _ + / " .OOOOOOD+OO .1I16+0D+04 " + / . OOOOOOD+OO -1.7707+9 2.300553 .4417730+04 .258104D+04 S0RT(chi"-2/^eg| of free) ia 1.5945  2 5 0 0 -L  2000 5500  ^5550  5600 5650 5700 Energy (keV)  5750  5800  FIGURE 4.6: THE DOPPLER FIT OF THE 6092 KEV, SINGLE ESCAPE PEAK.  8000 Background area 102929.7±320.8Z66 Triangle area 13972.7B±46S.B626 Peak Area 2651.205* 199.5765 • total Area I6623.98i128.934  7500 7000 H 6500 00  6000 o o  5500 5000 4-500 4000 3600  .  3650  3700 . 3750 Energy (keV)  FIGURE 4.7: THE DOPPLER FIT OF THE 3684 KEV PEAK.  380.0  3850  Table 4.7: The Gel energy resolution measured as a function of energy. Energy (keV) ' 75.24799 89.212 102.406 121.437 265.7 269.3 400.1 405.6 .  661.66 846.9 1173.238 1 173.238 1293.69 1332.502• 1332.502 • 23.41.2 2474.4 ,  4572.97 5083.97 5594.97  FWHM (keV) 1.38 .  1.33 1.33 1.35 1.47 1.44 1.65 1.64 1.88 2.12 2.69 2.57 2.75 2.81 2.75 4.12 . 4.12 8.72 8.35 9.16  4.6 How the y-ray Time Spectra were obtained The four router signals of the May 1996. experiment were histogrammed and summed using various conditions to produce time spectra of electrons and the following y-rays: 4439 keV from C; 3684 keV and 3854 keV from C ; and 6728 keV and 7012 12  ,3  keV from C . 14  The electron time spectra were used as a "control. The E l time spectrum was formed by applying the condition that both Gel and El had fired. The E2 time spectrum was formed similarly. These two time spectra were fit using Equation 4.5 from Section 4.3 using 4.3% as the percentage of electrons produced from muons stopping in carbon.  88  For each y-ray, two conditions were applied to the time spectrum. One was that only Gel had fired and the other was that the event occurred within an energy window around the peak of interest. This resulted in the raw y-ray time spectrum. To correct for the background underneath the y-ray peak, the energy window was shifted to energies above and below the y-ray of interest. These shifted windows were then used, with the Gel only firing condition, to produce two background time spectra. These background time spectra were consistent, so either time spectrum could be subtracted from the raw time spectrum of the y-ray. This subtraction was done after the background time spectra was properly normalized. The result was the y-ray time spectrum. To look for hyperfine effects, each y-ray spectrum was rebinned and divided by a rebinned E l time spectrum. These spectra were rebinned into bins 90 channels wide, to reduce noise. The number 90 was determined through fast Fourier analysis of the raw spectrum: Before being divided each y-ray spectrum was fit, using PLOTDATA, to  N't) = Ce~ + B , Dl  .  (4.9)  This fit was done so that the flat background, B, could be subtracted from the y-ray time spectrum before being divided by the rebinned E l time spectrum. These results are presented in Section 5.3. Another method to look for the hyperfine transition was to divide two y-ray time spectra and look for a difference. The results of these ratios were harder to quantify because of the poor statistics, so these results were not presented.  89  4.7 How the Ge Detector Acceptances were Obtained To determine the acceptance of Gel, y-ray peaks from. Eu and Co radioactive 152  60  sources were used along.with muonic x-rays from p/Au. To calculate the acceptance of the y-ray sources Equation 4.10 was used.  30000  LA E c  p  where A is the area of the peak of interest, f,s is the number of scaler events that did not make it to tape, fsA is the self absorption factor, clock is the number of.pulses generated from a 30kHz pulse generator, L is the livetime, Ac is the known activity of the source, and E is the emission probability of the source. The correction factor fsA is calculated p  by:  '  f =e^. SA  ,  '-  .  (4.11)  .  where X is half of the thickness of the source, p is the density of the source, and p is the mass attenuation coefficient. The target was made of uniform material, so the cases where muons stopped in the target but off center and produced a strongly absorbed y-ray, it was assumed that the amount of absorption would average out. The livetime was calculated by  90  (4.12)  where clock • inh is the number of pulses generated by the pulse generator in coincidence with the inhibit signal of Section 3.8. In the cases where muonic x-rays were used, their acceptances were calculated by Equation (4.13).  Accept =  A f l s f s A r  .  x  (\,2-3-0 -O -O )LE XNi  XFe  xc  , '  .  (4.13)  p  where 1 • 2 • 3 is the number of 51 • S2 • S3 events read by a hex scaler and O is the x  number of muon stops in other materials like Fe, Ni, and C. The values for E for the 2p /2 —> Is 1/2 and 2pm —> Is 1/2 muonic Au x-rays were 3  p  found in a paper by Hartmannf ]. The values of E for the other muonic Au x-rays were 110  p  calculated using a Muon Cascade program['"]. The program was used to calculate the emission probability for the following transitions: 3d3/2 3d/2 , 4f/2 —> 3d 3  7  5/2  , 5g  7/2  —> 2pm,  3d5/ —> 2  2pyi,  4fj/2 —>  —> 4f , and 5g / -> 4f . The energies of these transitions 5/2  9 2  7/2  are: 2472.4 keV, 2343.1 keV, 899.6 keV, 869.1 keV, 405.6 keV and 400.1 keV respectively. As an estimate of the error in these calculations, the same program was used to calculate the emission probabilities for the following transitions: 3 -> 2, 4 —> 3, and 5--» 4. The emission probabilities for these transitions have been measured[' ]. 10  The difference between the calculated emission probabilities and the measured  91  probabilities was used as the error in the c a l c u l a t i o n o f the 6 more s p e c i f i c e m i s s i o n probabilities. T h e s e e m i s s i o n probabilities.are listed in T a b l e 4.8. O  x  was calculated as  Oi =  •  fiS  A  (4.14)  (Accept)LE  for the Fe and N i x-rays. The values o f E for the Fe x-ray was found in a paper by p  112  F.J.Hartmann[  113  ] and for the N i x-ray was found in a paper by T. von Egidy[  ]. The  carbon x-ray (75 keV) was in a region where the acceptance was not well known for G e l , so it was calculated by the use of Ge2 values. The value o f E for this x-ray was found in p  a paper by J.L Lathropf ]. Since that 75 k e V x-ray was usually below the normal data 114  taking energy threshold, the Oxc value was multiplied by the following threshold factor:  A• threshold/actor =  A•  TR  (4.15)  1 • 2 • 3 - 1 • 2 • 3 • inh J HTR  where L T R indicated the values were obtained from the low threshold liquid nitrogen run, and H T R indicates that the values were obtained from the high threshold liquid nitrogen run. Seeing that Equations (4.13) and (4.14) depend on each other, they were calculated in a self consistent way. The resulting acceptances are presented in Table 4.9.  92  These acceptances were not enough information to obtain a good fit of the energy vs. acceptance curve, so a few acceptances from another experiment  were used.  These acceptances were obtained with the same detector but at a different distance. So to merge the acceptances, the above acceptances and the external acceptances were converted into absolute efficiency s by Equation (4.16).  s=  accept Q.  (4.16)  where Q is the solid angle, which was calculated from [ ] 104  i  R  2 Y  1-  2  1+^ f  J  (4.17)  2  v.  J  where RQ is detector radius, and d is the distance the detector is away from the source. Then since the'energies related to these efficiencies were greater than 500.keV, the efficiency vs. energy curve was fit to  s = aX  ai  (4.18)  where a and a are free parameters, and E is the energy. This fit is shown in Figure 4.8. L  2  Then Equation 4.16 was used to convert the efficiencies back to acceptances.  93  In-the case o f Ge2 the acceptance was calculated from y-rays from 2 2  Na,  l 3 j  l:i2  Eu,  6 0  Co,  B a , and from p ' A u x-rays. These calculations were performed in the same  manner as above, except no external information was used, and hence, there was no need to convert the acceptances into efficiencies and then back into acceptances. Table 4.10 gives the values o f these calculated acceptances. Since the 511 k e V y-ray can come from more than just the " N a source, the background 511 keV y-ray area was subtracted from the raw area. The background corrected area is listed in the table. Since the Ge2 acceptances covered a greater dynamical range they were fit to:  • s = a E +a,e- ' ai  x  a>l :  + a e " ° ^ +a e"" 5  7  ,£  .  (4.19)  '  Figure 4.9 shows what that fit looks like.  94  Efficiency  Ge1  •iry  A1 A2 AJ A4  +/+/" +/+/-  0.17790 D-01 -0.87172D+00 0.000000+00 O.OOOOOD+00  0.326310-03 0.418890^01 O.OOOOOD+00 O.OOOOOD+OO  o 10 c CJ  LU  10  AS A6' A7 A3  0.00000 D+00 O.OOOOOD+00 O.OOOOOD+00 O.OOOOOD+00  SQFfT(chi"2/deg  10  10  O.OOOOOD+00 O.OOOOOD+OO O.OOOOOD+00 O.OOOOOD+OO  •+/+/+/-  of free)  J-1  10 •  is  .0.9136  10'  Energy (MeV) FIGURE 4.8: THE G E I EFFICIENCY.  able 4.8: The muonic x-ray transition probabilities. Energy (keV) Element Transition E 102.4 N 2p -> Is 0.70 ±0.07 400.1 Au 5g /2 -». 4f /2 0.39 ±0.06 405.6 Au 0.30 ±0.06 5g7/2->"4f /2 869.1 Au 4f -> 3d / 0.44 ± 0.04 899.6 Au 0.31 ±0.04 4f -> 3d /2 2343.1 Au 3d5/2 -> 2p /2 0.52 ±0.08 2472.4 Au 3d -> 2pi/2 0.29 ±0.08 5594.9 Au 0.333 ±0.019 2pi/ — l S i / 2 5764.89 Au 0.559 ±0.032 2p3/2^1Sl/ D  9  7  5  7/2  5  5/2  2  3  3  3/2  2  2  10  Ge2 Acceptances  10" Al A2 A3 A4  •+/V" +/+/-  0.24 655D-03 -0.87 793 D+00 -0.936200-01 0.14721D+02  O.OOOOOD+OO 0.000000+00 0.207S9D-03 0.55206D-01  10" ' O O CL CD O O < A5 A6 A7 AS  •10"  0.170930-02 0.Z1629D+01 0.207890-03 0.578320-01 SQRT(chf 2/deg of free) is 4.54S3  10" Energy (MeV)  10  10  FIGURE 4.9: THE GE2 ACCEPTANCES.  Table 4.9: The acceptances for Gel Energy (keV)  Area  964.055 1112.087 1173 1333 1408.11 Energy (keV)  20649 17843 32751 30141 23288 Area .  869.98 899.14 • 2341.2 2474.2 5594.9 • 5764.89  7955 5678 3442 2352 1268 1813  fls  fsA  Clock  L  Ep  Activity  Acceptance (x 10" ) 5.39 4.96 5.12 4.71 •' 4.15 Acceptance (x 10 ) 6.8 6.9 2.3 2.9 1.3 1.1 4  4.47 4.47 1.11 1.11 4.47 fls  1.17 1.16 1.00 1.00 • 1.14 fsA  43275573 43275573 30427338 30427338 43275573  0.146 0.1356 0.9989 0.99983 0.208 E  3483064 3483064 98362 98362 3483064  1-2-3  0.27 0.27 0.71 0.71 0.27 L  Oxc  OxFc  1.61E+08. 1.61E+08 1.61E+08 1.61E+08 1.61E+081.61E+08  0.53 0.53 0.53 0.53 0.53 0.53  0:44 0.31 0.52 0.29 0.3332 0.5588  3.29E+07 3.29E+07 3.29E+07 3.29E+07 3.29E+07 3.29E+07  7.78E+06 7.78E+06 7.78E+06 7.78E+06 7.78E+06 7.78E+06  p  OXN,  J  1.27 1.27 1.27 1.27 1.27 1.27  1.16 1.16 1.09 1.09 1.09 1.09  4.56E+07 •4.56E+07 4.56E+07 4.56E+07 4.56E+07 4.56E+07  96  Error (x 10" ) 0.09 0.08 0.04 0.03 0.06 Error (x I 0 ) 2.0 2.0 0.7 1.0 0.4 0.3 4  J  Table 4.10: The acceptances for Ge2.  Energy (keV)  •Area •  30.75 35.2 53.161• 80.3051 244.6989 276.4 302.8527 344.2811 356.0146 383.8505  15547 5213 664 10636 12756 1539. 3620 41424 10719 1363 138310511 8703 489  1'LS  fsA '  Clock  Activity  L  Acceptance x 10 J  511  964.055 1112.087 1274.542  1173 1333 . 1408.11 Energy  15802 14191 11023 Area  400.1 405.6 869.98 • 899.14 2341.2 2474.2 5594.9 • 5764.89  4380 3537 3869 2726 1494 1033 507 645  (keV)  1.23 1.23 1.23  1.0 1.0 1.0  1.23 4.47 1.23 1.23 4.47 1.23 ' 1.23 1.10 4.47 4.47  1.0 1.33 1.0 1.0 1.28 1.0 1.0 1.0 1.16  1.10  1.15 1.0  1.10 1.10 4.47.  1.0 1.0 1.13  ks  fsA  16192355 16192355 16192355 16192355 43275573 16192355 16192355 43275573 16192355 16192355 30427338 43275573 43275573 30427338  0:57 0.57 0.57 0.57 0.27 0.57 .0.57 0.27 0.57 0.57 0.71 0.27 0.27 .0.71  0.955 .0.222 0.022 0.3673 0.0754 0.0717 0.1832 '• 0.2652 0.62 0.0893 1.805 0.146 0.1356 0.9993  126013 • • 126013 126013 126013 3483064 126013 126013 3483064 126013 126013 3023 3483064 3483064 3023  30427338 30427338 43275573 1-2-3  0.71 0.71 0.27 L  0.9989 0.99983 0.208 E  .98362 98362 3483064  1.61E+08 1.61E+08 1.61E+08 1.61E+08  0.53 0.53 0.53 0.53 0.53 • 0.53 0.53 0.53  p  Oxc  5.2 7.4 9.5 9.1 7.3 6.8 6.2 6.53 • 5.5 4.8 3.9 2.74 2.42 2.47  •  OXF=  PxNi  1.52 1.53 1.16 1.16 1.09 1.09 1.09 1.09  1.61E+08 I.61E+08 1.61E+08 1.61E+08  0.39 0.3 0.44 0.31 0.52 0.29 0.3332 0.5588  3.29E+07 3.29E+07 .3.29E+07 3.29E+07 3.29E+07 3.29E+07 • 3.29E+07 3.29E+07  7.78E+06 7.78E+06 7.78E+06 7.78E+06 7.78E+06 7.78E+06 7.78E+06 7.78E+06  4.56E+07 4.56E+07 4.56E+07 4.56E+07 4.56E+07. . 4.56E+07 4.56E+07 4.56E+07  1 3  C and the  1 4  C y-rays were calculated in a very similar manner,  in the sense that many of the variables are the same, as the acceptances o f Section 4.7. Equation 4.20 was used to calculate the yields.  Yield =  (\-2-3lAccept)LC  F  '  0.1 0.4 . 1.0 0.3 0.2 . 0.3 0.1 0.09  0.1 0.2 0.2 0.06 0.05 0.03  -4  4.8 How the j^ray Yields were obtained The yields of the  1  2.5 0.2 2.22 0.03 1.96 0.04 Acceptance . Error x 10" x IO .... 5.6 . 2.0 5.9 . 2.0 3.3 0.9 3.3 1.0 1.0. - 0.3 . 1.3 0.5 0.5 0.1 0.4 0.1 1  1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27  Error  x 10"  (4.20)  97  where A is the area o f the  i j  C or the  l 4  C y-ray of interest, Accept is the acceptance at that  energy calculated using either Equations 4.18 or 4.19, and Cp is a correction factor for the number o f muon stops. The correction factor is necessary in this case because the target was larger than the defining counter S2. The correction factor was found by calculating two acceptances o f the 102 k e V muonic nitrogen x-ray. The "actual" acceptance was found by using Equation 4.19, whereas the "improper" acceptance was calculated by using Equation 4.21.  AflsfsA  (4.21)  This calculation was performed using the Ge2 data from the l o w threshold run. In Equation 4.21, A is the area of the 102 k e V peak. The value o f E for this x-ray was p  found in a paper by J.L Lathropf ]. The correction factor C was then found from the 114  F  "improper" acceptance divided by the "proper" acceptance. The yields obtained in this manner are presented and discussed in Section 5.4. In the raw energy spectrum, the 6092 k e V peak was contaminated by the double escape peak from the 7010 keV peak. So the area used to find yield o f this y-ray was found from a spectrum which had the following cuts: C S A did not fire and E l did not fire. T o correct for accidental firings o f either o f these two detectors, the area o f the 6726 k e V peak was compared before and after the cuts. After this comparision, it was. found that the 6092 yield had to be divided by 0.97 ± 0 . 1 2 .  98  Chapter 5: The Results 5.1: The Hyperfine Transition Rate Results from the Neutron Experiments Tables 5.1 and 5.2 show the results of the hyperfine transition rate from the neutron experiments for the November 1994 experiment, compared to theoretical calculations and previous experiments. Figures 5.1 and 5.2 show the fit time spectrum for LiF and Na respectively. Note that the theoretical values are listed with respect to the hyperfine element of interest and not necessarily by compound. In the case of compounds with two hyperfine elements, the hyperfine element of interest was underlined. The previous results used various techniques (neutron detection, y-ray detection, and uSR). By comparing the muonic hyperfine transition rates in Table 5.1, for metals and nonmetals, one does not see a chemical compound effect on the hyperfine transition rate. Overall, most of the results of this experiment agree with or are very close to theoretical calculations, with the exceptions of NaH, Na, and P. In the case of Na, and NaH, the discrepancy between this experiment and previous experiments could be due to the fact that the previous work was taken at a high rate. This could distort the time spectrum of the gamma rays that were detected. The results for Na and NaH, from this . experiment also do not agree with theoretical.prediction of Winston, it could be possible that the time of flight effects of the neutrons coming from Na are very different than the ones from Mg. This was first appearant when the F results were first analyzed. Originally the LiF results also had its S and Xo (time of flight) parameters fixed to the Mg results. Then these parameters were allowed to vary. It was found that the value of the  99  hyperfine transition rate in F changed from 6.3 ± 0.3 us" (with Mg values) to 5.6 ± 0.2 1  us" (varied S and Xo). The residuals for these two cases are shown in Figures 5.3 and 1  5.4. The reason for this change, is that the underlying assumption that the neutron energy spectrum for p"F and u'Mg was wrong. Now this assumption may not be as bad for the other cases indicated in Table 5.1 with an ). The error due to the estimation of the a  amount of Li in LiF is small as A and H did not change when Li was not corrected for. For the capture rate asymmetries that are listed in Table 5.2, all the measured values agree with the Primakoff model of muon capture(which was described in Section 1.3) and with the results of Winstonf ] (other results were not listed as they were of single 26  transitions). For the asymmetries for Na and NaH, Primakoff and Uberall gave no value, but typically their results are greater than BLYP; our result is about three times that of BLYP. For the hyperfine transition rate in red P we give an actual value, unlike previous experiments which have given contradictory limits.  Compound  Theoryf ]  LiF  5.8  26  NaF  Previous Work 5.8 ± 0.8 6.3 ± 1.8 4.9 ± 1.2  |"1 26  5.6±0.2  [ 1. 78  (CF )„  5.1 ± 0 . 4  2  Na  14  15.5 ± 1.1 I"] 86  NaH  47 ± 8 ) a  42 ± 7 ) a  NaF  8.4 ± 1.9  Al LiAlH  T h i s Experiment  41  41±9[ 1  58  A  83  36 ± 10 ) a  37±9 ) a  4  RedP  h  » A . [  7  f  8  48±5 ) a  A-»A„r l* 6  LiCl  8  ecu  8  15 ± 2 9 )  K  22  25 ± 15 )  6.5 ± 0.9 [ ] 78  14 ± 27 ) b  b  b  nuclei. Research is still on going on these targets. b  ) These results are obtained by a special method outlined near the end of Section 4.2.  * A_~ 1.1 us'  1  100  LiF 10000 8000  ^LT T P i T  l P  u  ^ 1  n  £.6000 D C 0  CL  v 4000  A H F G P Q  0.289792 0.55943D-02 5.750000 0.49400D-03 16.790000 0.45800D-03  s  If)  8 2000 o  -2000  X  0.67945D-03 1905.023770 103.750000 5.380909 5.304629  0  200  +/+/+/-  +/-  +/+ /+/-  O.19309D-O5 6.460495 0.000000 0.175339 6.165026  0.006293 0.24930D-03 0.000000 +/-• O.OOOOOD+00 +/0.000000 +/O.OOOOOD+OO +/• SQRT(chr Z/deg of free) is 1.1461 .% of Carbon is 0.3763716722169554 X of Lithium is 1.151047758732232  . 400. 600 Time (ns)  800  1000  FIGURE 5.1: THE TIME SPECTRUM OF LIF, WITH THE DECAYDIVIDED OUT.  Na i  _ J  '  _i  :  i  ^10000 TJ  CL X  D  <D \  00  c"  5000-  B S X A H  C Z! o  Li  F G  .  0 0  200  T  400 Time  0.84746D-03 '. + / 0.12711D-05 2920.718607 . 4.662171 +/106.170000 0.000000 "+/4.630000 0.000000 +/4.220000 0.000000 +/" 0.224454 0.016635 +/0.47297D-01 0.484900-02 +/5.56OO00 0.000000 +/0.49400D-03 O.OOOOOD+OO +/-. SQRT(chP2/dea of f res) ia 1.0997 % of Carbon is 0.283202910+592802  600. (ns)  FIGURE 5.2: THE TIME SPECTRUM OF N A , WITH THE DECAY DIVIDED OUT.  800  1000  LiF TOF fixed J  :  L  400  200 o  OH -200  -400 H i  1  200  4.00 Time  :  1  . 600 (ns)  r  800 '  1000  FIGURE 5.3: THE RESIDUALS OF THE L I F TIME SPECTRUM WHEN TIME OF FLIGHT WAS FIXED.  LiF. TOF varied J  i  L  400 H  200 o  Li_  -200 H -400i  200 -  :  r  • 400 Time  (ns)  600  800  1000  FIGURE 5.4: THE RESIDUALS OF THE LIF TIME SPECTRUM WHEN TIME OF FLIGHT WAS VARIED.  Na 400  200  -200 -400 200  400' 600 Time (ns)  800  1000  FIGURE 5.5: THE RESIDUALS OF THE N A TIME SPECTRUM.  able 5.2: The capture rate asymmetry. Compound BLYP[ ] Primakofff, ]  Uberall [ ]  Previous work[ ]  LiF  0.361 0.04 (n) 0.25 1 0.04 (y) 0.29 1 0.02 (ny)  26  (CF ) Na' NaH Al LiAlH RedP LiCl 2  n  4  26  2y  0.24  0.36 '  0.36  0.24 0.08 0.08 0.09 0.09 0.16 -0.06 ( C1) -0.06 ( C1)  0.36  0.36  0.14 0.14 0.22 -0.10 ( C1)  0.22 0.22 0.25  -0.05  -0.07  J/  26  This Experiment 0.29810.006  0.35 10.01 0.22 ± 0.04 0.25 10.05 0.13 10.04 0.15 10.04 0.21 10.03 -0.03+0.06  35  37  CC1 K  4  -0.03 10.06 -0.08010.055  103  The liquid nitrogen (LN2) did not give a hard number for the muonic hyperfine transition rate as implied in Section 4.3. Instead a slight change in the muon lifetime was looked for. Table 5.3 gives the measured lifetimes of p." on LN . of u" on H 0 , and of the 2  2  positive muon, for two different methods. This Table also gives previous work. As .one can see the results of the summed method for the lifetimes agree or are close to the previous work by Suzuki et al., except for the case when this experiment detected neutrons from u~ on LN2, whereas in the single muon method, all the e detection results 1  are systematically about 32 ns too low. There is a controversy over the lifetime of the muon in nitrogen as one can see from Table 5.3. Since the measurement preformed by Martino[ ] did not take data until 3 us after the muon is stopped in the nitrogen, a 117  -  possible explanation is that the muon is in the upper hyperfine state in Suzuki's measurement and in the lower hyperfine state in Martino's measurement.. Morita[ ] has 30  calculated these capture rates to be 0.109 us" for the upper.state and 0.060 us" for the 1  lower state.  '  1  '  , Table 5.4 shows the differences in the lifetimes depending oh which type of particle is detected. One can see that the H 0 results are.almost consistent with zero, 2  where as the LN2 results are clearly not consistent with zero. The fact that lifetime is longer when the electron time spectrum is being measured than when neutrons are used to measure the lifetime, implies that the capture rate is higher from the upper hyperfine level. This is qualitatively consistent with the above mentioned calculation of Morita.  104  One thing is clear; if an accurate time spectrum is needed, the data taking rate has to be very low (as was the case with Suzuki et al.), otherwise electronic artifacts distort the measured lifetime.  .  Table 5.3: Muon lifetimes in nitrogren and oxygen. Beam/ Particle Single muon Summed muon Target detected lifetime (ns) ) lifetime (ns) ) Neutron u" L N 1841 ± 5 . 1869 + 5 • Electron . 1872 ± 2 u." LN2 1905 + 3 a  Previous work lifetime (ns)  b  :  2  1906.8 + 3.0 [ ] (Suzuki) 1940.5 ±2.8 [ ] (Martino) l9  117  u" H 0 u/H 0 u H 0. 2  2  +  2  a  b  Neutron Electron Positron  1752 + 8 1766 ± 4 2163 ± 4  1787 + 9 1802 ± 4 2206 ± 4  1795.4 ±2.0 [ ] 2197.03 ± .04 [ , ] 19  59  118  ) Time spectra from routerl with no hits in other routers. See Section 4.3. ) Time spectrum formed from adding all four router spectra. See Section 4.3.  able 5.4: The difference between detecting electrons and neutrons Single muon lifetime Summed muon lifetime differences differences L N electron-neutron 31 ± 7 36 ± 8 H 0 electron - neutron 14 ± 12 15 ±.13 2  2  5.2 i*Ray Identifications and Energies Tables 5:5, 5.6, and 5.7 show the energies of the observed y-rays seen during the u" L N experiment. Each of these y-rays have a code beside them indicating under which 2  conditions these y-rays were observed. The P code means that the y-ray has been seen in. the energy spectrum where there has been a time cut placed on the prompt peak. The D code indicates that the y-ray has been seen in the decay part of the time spectrum. The B code means that the y-ray has been seen in the time < 0 part of the time spectrum  105  '•>  or the background part of the time spectrum. The peaks without a code were seen in either the raw spectrum or the spectrum with no electron counter firing. Figure 5.6 shows the time spectrum for Gel and these three time cuts. In the tables, if there is no value in the error column, it means that the peak could not be fit to a Gaussian, and the centroid of the peak was estimated with the cursor. The errors are simply statistical errors from the. fit. The Compton suppressor, which had a hardware threshold of approximately 300 keV, was turned on or off in software to identify single escape and double escape peaks. •  <J  Decay  cut-  ^Background  c u t x i  z: o— O O -Prompt c u t  .200  400  800  .  1000  1200  1400  1600  • . 1800  2000  TDC Channel Number FIGURE 5.6: T H E TIME CUTS ON THE G E I ROUTERI TIME SPECTRUM FOR MUON CAPTURE ON .' (1 CHANNEL = 4.93 NS).  H  N  In the tables x-rays from uC, uN,.uFe, and uNi atoms were seen. The N x-rays are from the target. The C x-ray is from the carbon in the scintillators. The Fe and Ni x-rays are thought to be from the u-metal shield around the target. Not all of the.np -> Is Ni x-rays energy values are found in the literature, so they were calculated by using the  106  2p —> 1 s literature values and a simple Bohr atom model. These calculations were done only for identification purposes. That is why the tables do not include the literature values o f the x-ray energies: The (n,n') reactions also occur, since once the p" captures, it w i l l excite the •nucleus and neutrons will be emitted. There is also a sea of background neutrons from the pion production targets. A l l o f these neutrons have an M e V or two o f kinetic energy which is enough to excite nuclei o f nearby materials. These nearby materials then deexcite by giving off y-rays. Gamma rays from 27  A l ( n , n ' ) are seen. The  1 4  127  I(n,n'),  72,78  G e ( n , n ' ) , N ( n , n ' ) , and l4  N reactions were from neutrons hitting the target. The  reaction y-rays are from neutrons hitting the Compton suppressor. The  7 2 7 8  1 2 7  I  G e reactions  are from neutrons hitting the detector, whereas, the A 1 reactions are from neutrons 27  hitting the detector stand components. A t T R I U M F , when the cyclotron beam is on there are also thermal neutrons produced. These thermal neutrons cause (n,y) reactions. In this experiment the following (n,y) reactions were seen: 1  127  I(n,v), ' G e ( n , y ) , Fe(n,y), ' C l ( n , y ) , A l ( n , y ) , and 70  74  56  35  37  27  127  H(n,y). Again,  I(n,y) are from neutrons hitting the Compton suppressor , the  ' Cl(n,y) are from neutrons hitting the black P V C tape used to hold the target together , and  70  ' G e ( n , y ) are from neutrons hitting the Ge detector. The Fe(n,y) y-rays are 74  i6  possibly from the p-metal shield or the stands. The Al(n,y) was also from neutrons 27  hitting the stands. These (n,y) identifications were further confirmed by checking the branching ratios of these y-rays [  108  ] and by the use o f the acceptances o f Section 4.7. A  Actually the capture cross section for thermal neutrons in C1 is about 100 times larger than for C l , so the Cl(n,y) reaction is not seen. 3  35  i 7  j7  107  more complete analysis of these (n,n') and (n.y) reactions can be found in the M.Sc. thesis[ ] of E. Gete. 119  ;  ,  . . . . .  '  Some background y-rays were also seen in these tables. Those from ~" Th are from a bottle of Th that had been left in the area as a calibration source. Those from l:)2  Eu have been found in the concrete at TRIUMF (and confirmed independently by the  TRIUMF Safety Group).- They come from neutron capture in a heavy aggregate used for the concrete. The Co is probably via spallation reactions on copper in the quadrupole 60  coils. Finally, y-rays from  ' c which occur from muon capture on  1213 14  l 4  N are also seen.  The C and C lines are from one and two neutrons being ejected after muon capture. 13  12  The energies of the C y-rays have been measured previously to a very good accuracy , J  [ ], so they will not be discussed. On the other hand the energies of the C y-rays are , 106  14  not so well known. The 7.0 MeV full energy (FE) peak was fit to a Doppler broadened line as discussed in Section 4.5. The resulting energy of this peak is listed in Table 5.8. It also lists the single escape (SE) peak, which can be used to estimate the energy of the full energy peak, by adding the electron mass to the y-ray energy. These two measurements are averaged to give a y-ray energy and this result is consistent with, but more precise than, previous work. The same method was applied to the 6.7 MeV line, which yielded a'-y-ray energy close to the previous work as shown in Table 5.8.. For the 6.0 MeV peak, 2 models were used to describe the peak and its background lines, as discussed in Section 4.5. These two models are first averaged and  then the result is averaged with the single escape peak result. T h e result for this y-ray is also consistent with previous work, as s h o w n in T a b l e T a b l e 5.5:  5.8.  T h e y-rays seen in the low energy r e g i o n o f G e l .  Measured Error Energy (keV) (keV) 29.26  Area  Error  Lit.Value  (counts)  (counts)  (keV) 27.4  Identification  127  l(n,y), pedestal  D,B,P  Eu-  D,B,P  33.26  0.02  5713  262  32.89  , M  54.77  0.08  12419  1219  52.37  ,2  75.95  1835.5  Observed  ,  .  B  'l(n,y)  75.8 n'C x-ray 2p -> 1s  D,B,P  •101.9 H N x-ray 2p -> 1s  P„D,B  121.9 n'N x-ray 3p -> 1s  D,B,P  103.148  0.002  122335  672  122.138  0.005  27647  389  128.769  0.008  14660  330  128.091 n"N x-ray 4p -> 1 s  D.B.P  131.90  0.02  7093  687  131.167 |TN x-ray 5p -> 1s  D,B,P  198.85 • 0.04  6963  694  134.14  203.23  936  266.11  2221.3  198.35 °Ge(n;y)  D,B  202.94 " ' K n . n ' Y j  D,B  7  265.705 n'Fe x-ray 3d /2 -> 2 p / 248.9  259.32  259.3  269.51  .945.8  27  AI(n,y)?  27  AI(n,y)?  269.427 n'Fe x-ray 3 d  301.91 308.56  0.02  .15789  1636  0.03  7265  492  374.19  1051.8  417.79  5703.3  3 / 2  0.02  14364  ..  617  309.97 n'Ni x-ray 3d -> 2p 316.9  Ge(n,y)  74  0.03  478.07  11490  '686  2348.3  '  P,D,B  417.95  127  420.84  "'KM  l(n,n'y),  127  l 5/2*-> 5/2  +  ..  P.D.B  :.  439.991 ' N a 5/2*-> 3/2* J  D.B .  P,D,B  442.9  12  ' l ( n , n ' y)  D,BP  445.2  74  Ge(n,y)  B.  472.207  27  AI(n,ay) Na 24  477.605 'Li"  490.87  493.6  , M  Eu  491.66 0.01  944506  1708  .563.46 108103  25276  511.0034 e*e' annihilation  593.3  1375.3 0.05  3002  608.353 1026  P.D.B D D  P,D,B P,D,B  12  'l650->58  595.8 " G e ( n , n ' )  609.45  -  D  562.93 0.11  600.35  618.51  P,D,B  D,B,P.  446,88  593.25  D  /2  B  442.88  511.02  -> 2 p i .  D  421.69  472.35  D  5  301.9 " ' K M  313.54  440.09  2  5  248.92  ,3  Ge(n,y)  618.5 " ' K n . n ' . y )  P,D,B  ,  P,D,B P.D P,D,B  109  Measured Error Energy (keV)' (keV) 628.56  .  Area  Error  (counts)  (counts)  0.04  5030  Lit.Value  Identification  Observed  (keV)  874  628.6 "'Kn.n'Y)'  P.D.B  641.74  P,B  659.04  1154.7  658.9  687.63  ,2  688.674  693.23  'Kn.n'y)  , w  Eu->  Sm  1 w  .  D  692.03 F e ( n . v )  D,B  691.3 "Ge(n,n') • . 966  728.03  962 0.04  .  30  718.3  , U  728.34  4131  988  778.90  0.08  2126  ' 678  811.55  .0.39  5189  1565  , ,835.38  0.06  5147  579  14  B .  •  N(n,n'y) •  •  '  AI(n,n'Y)  P;D,B  846.93  0.02  10786  314  963.88  0.07  3302  283  964.055 ' ~ E u - > " S m  1014.54  0.03  6168  260  1014.45 AI(n,n'Y)  864  221  2820  578  1085.96  0.07  1822  261  27  846.754 ~ M n -> ~ F e  P,D,B  846.754 ^ F e ^ . n ' y)  P,D,B  220  1099.36  675.8 0.05  2,  1146:45  580  1164:74  1236  249  •  1044.2  0.01  21725  332  1224.02  0.32  1470  1075  '.  ,,5  P,D , M  Sm  B  ln(n. ) Y  1112.087 ' ~ E u - > 1 5 2 S m  1173.238  J5  CI(n, )  o u  Co  D,B  y  P,D,B  1222 '"Ge(n,Y)  P,B  1221.89 - A l , . . 1238.32  0.07  . 1897  1253.17  0.07  7863  528 10711  1257.20  0.06  . 2523  1274.56  0.04  5029  624 ••  255  P,B  1238.255 °Fe a  D,P,B  1253.01 LiTex-ray 2 p 1248  .  ,4  1 / 2  1274.542 " N a  .  0.01  64661  0.01  22223  .  487  1293.609 " A r  338  1332.501 - C o  D, B,P D,B,P  3 / 2  .  ->  ^s  m  D,B,P P,D,B  1274.54 " E u  1332.53  H > 1s»2  Ge(n,y)  1257.21 u'Fe x-ray 2 p  4  1293.59  P,D,B  P,D  1085.8 ' " E u ->  1164.72  1173:20  :  1021.7  '1097  2270  D,B  , ;  1044.2 - A l  1094.96  D.B.P D,B,P  480  843.76  '  Mn  i 4  7456  0.14  B B  834.2 "Ge(n,'n")  0.06  1044:30  P,D,B  778.92 ' " E u - > ' ~ S m  838.8  .  .  844.05  1022.57  D,B  744.7 "'Kn.n-y)  '  /  P,D,B  w  718.83  1112.15  '  P,B  644.54  744.81  '  P,D,B ,•  P,D,B P.D.B  .  Measured Error Energy (keV) (keV) 1345.81  Area  Error  Lit.Value  (counts)  (counts)  (keV) 1345.5  1368.69  0.07  2080  242  1377.82  0.07  2390  217  1408.19  0.03  5947  315  Identification  Observed  23  Na(n,y)  1368.675  27  A I ( n , a ) N a ->  D  1408.011  , M  24  2 4  Mg  D,B D,B  Eu->-  I M  Sm  D,B  1424.40  D  1427.66  0.10  36511  8520  1427.033 (i'Ni x-ray 2 p  1432.95  0.03  .15332  2655  1432.580 H~Ni x-ray  1454.58  0.09  1687  270  1460.99 436  1514.78  647.3  704  575  D.B.P  ln(n,y)  D  , w  1612.78  5S  E u -> 152Sm  D  Fe(n,y)  D  1622.51 'AI(n,y)' 2  1631.46  1633.5 " N e -  1725.33  0.11  4051  1586  1739.46  0.23  3784  980  1757.93  0.12  1725.29 F e ( n , y )  D  n'Ni x-ray 3 p  ^  1764.3 0:04  D,P,B  M  3 / 2  -> 1s  4396  226 •  1809.51  0.13  1677  310  1847.48  0.23  1532  3650  P b  1779.03 'AI(n, )  D,B  1779.03 " A I - > ' ° S i  D,B  2  Y  1808.7 ~ M g  D  n'Ni x-ray 4 p  3 / 2  -> 1SI  / 2  1897.94  n'Ni x-ray  1919.89  (i'Ni x-ray 6 p  -> 1 s ,  /2  1943.29  n'Ni x-ray 7 p - > • 1 s ,  /2  1950.88  n'Ni x-ray 8 p  1958.27  n'Ni x-ray 9 p  5p3/2.-» 1 s 3/2  •900  1949  23  2211.1  27  3/2  -> 1 s „  3/2  -> 1 s ,  Na(n,y)  n'Ni x-ray complex 2211.45 0.01  6938  241  2243.64  AI(n,n'y)  2223.247 'Hfn.y)  •  1 / 2  3Q  1950.40  D  ) / 2  D  1764.83  2223.18  P,D,B  -> 1s,/2  D  1622.26  1778.90  m  1528.5 0.01  V2  D,B,P  2  Ar  o u  1507.5  1529.38 1613.29  2p  -> 1s„  D,P 1460.859  1508.58  1 / 2  2  /2  D D D P,D,B  2240 'AI(n,y) 2  2312.73  5087  2312.593  2539.58  14  N(n,n'y)  D  2541.92 " N a  P  2614.04  0.10  2286  182  2614.42 — T | - > - * " P b  D,B  2753.58  0.15  1527  209  2754.03 - M g  ^PbCn.n'y)  2789.84  2792.79  14  N(n,n'y)  D,B D,B  T a b l e 5.6: T h e y - r a y s seen in the m e d i u m energy region o f G e l  Energy Area (keV) (counts) 2614.9  Error (counts)  Lit. Value Identification Observed (keV) . 2614.533 Th D,E3 w  2oe  2756.2 2832.9 2866.7 3090.4 3171.8 3342.2 3538.8 3593,1 3598.8 3684.9 3853.4 3910.7 3984.5 4219 4436.4 4734 4815 4935  P.B  Pb(n,n'y)  2754.03 379 4643  D,B D •  19 2863.94 CI(n,y) 524 3089.049 c SE "C SE C 35  D P,D D  13  13  226 17558 4963  7344  15 3591/12 AI(n,y) •• 27  245 3683.921 u 300 3853.17 C  P.D.B  Q  13  P.D.B  2092 4438.03  P.D.B  Table 5.7: The y-rays seen in the high energy region of Ge 1. energy Error (keV) 5026.8  Area  Error  Lit. V a l u e (keV)  Identification  5022 S E of 5533  Observed  nal  N(n,y)  5042.3  5048.2 S E of 5559.20  5085.6  5088.88 D E of 6110.88  5102.1  5107.39 D E of 6129.4 N  5105.88  127  35  l(n,y)  CI(n,y)  1 6  0.26  778  . 5266.2  117  338.3  5104.89 " N ( n , n ' y) 5269.22  5295.1  ,4  N(n,y)  5300.39 D E of 6322 N(n,y) ,4  5371  125  5404.6  396.3  5409.35 S E of 5920.35 of ^Fefn.y)  5503.9  435.2  5507.42 S E o f 6018.42 of ^Fefn.y)  5373.4 D E of 6395.4  5533.5 5556.3 5580.8 5595.2  23  Na(n,y)  5533.37 "N(n,y) Calced 1.7 3 4 8 5  5559.2 445  Calced  5614  140  5704  1038  ,2  'l(n,y)  5581 S E of 6092 C  D  H  5599.88 S E o f 6110.88 CI(n,y) 35  •  D  561.8.4 S E of 6129.4 N  D  5705 D E of 6727 " C  D  , b  112  energy Error (keV) 5814.1  Area  Error  Lit. V a l u e .(keV)  44.7  Observed  5811 S E of 6322 N(n,y) 14  5879.9 5921.4  Identification  5884.4 S E of 6395.4 Na(n,y) 23  0.4  445  87  5920.35 Fe(n,y) i6  . 5989 D E o f 7 0 1 0 " C -6000 6017.38  0.46  614  82  6091.23  0.93  2491  348  6018.42  calced  6110.88  6128.2  calced  6129.39  0.44  6255.6  478  101  387  D  CI(n,y)  3i  l b  N  6216.3 S E of 6 7 2 7 ' " C  P;D  6256.78 DE of 7278.82 of Fe(n,y) 56  6324.4 6393.3  Fe(n,y)  56  6092 " C  6109.8  6220.38  D  57.3  6322.39  ,4  6395.4  23  N(n,y) Na(n,y)  D E of 7413.88 of CI(n,y) 35  6471.2  6466.66 S E of 6977.66 CI(n,y) 35  6505.85  1.5  . 6617.4  1.7  6500.7 S E of 7 0 1 0 C  D  , 4  742  463  6619 CI(n,y) 3i  6612.83  6609.18 D E of 7631.18of Fe(n,y) D,B  6622.83  6623.58 D E of 7645.58 of ^Fefn.y) D,B  56  6701.6 6729.88  54 0.18  6766.9  1814  6701.85 D E o f 7 7 2 3 o f A I ( n , y ) 27  101  209  6727 " C  P,D,B  6767.82 S E of 7278.82 of Fe(n,y) 56  6892.0  D E of. 7916  6902.1  6902.88 S E of 7413.88 of CI(n,y) 35  6975.3  .6977.66 "Cl(n;y)  7016.78  0.49  7120.68  0.43  873  154  7120.18 S E o f . 7 6 3 1 . 1 8 o f F e ( n , y )  D.B-  7135.03  0.55  301  101  7134.58 S E o f 7645.58 of Fe(n,y)  D,B  7212.85 S E o f 7723 of AI(n,y)  D  7212.2 7278.4  7011.7  200  l 4  56  27  0.6  288  44  7278.82 ^Fefn.y) S E o f 7916  7412.4  0:8  407  89  7413.88  7631.88  0.19  1477  101  7631.18  st,  7644.88  0.17  792  67  7645.58  S6  7693.8  8380  3b  CI(n,y)  Fe(n,y)  ..  D,B B  Fe(n,y)  7693.42 'AI(n,y) 2  0.85  7790.9 7916.4  P,D 56  7404.0  7724.38  C  307  102  18.7 0.7  209  7723.85 .'AI(n,y) 2  7790.16  J5  CI(n,y)  60  128.2 •  113  Table 5.8: G y-ray energies in keV (only final averages include systematic errors). Peak type ; Energy Equivalent FE Previous work FE Same 7016.78 ±0.49 SE 6505.85 ± 1.5 7016.83 ±1.5 Average 7016.81 ±1.3 701 1.7 ±5.2 I106! FE Same \ 6729.88 ±0.18 SE 6220.38 ±0.44 6731.38 ±0.44 Average 6730.60 ± 1.0 6728.1 ± 1.4 [ ] FE model 1 Same 6092.7 ±1.3 FE model 2 6092.5 ± 1.1 Same ' . FE model 3 Same 6088.5 ±2.2 Average Same 6091.23 ±0.93 SE 5580.8 ±1.7 6091.8 ±1.7 Average 6091.5 ± 1.4 6094.5 ±3.2 [ ] 6092.4 ± 0.2. f l l4  106  106  106  5.3 The i^ray Time Spectra Results As explained in Section 4.6, the ratios of y-rays to electron time spectra were used to find a hyperfine transition rate effect. Unfortunately no effect was seen, due to lack of statistics in y-ray time spectra, as can be seen in Figures 5.7 and 5.9. These figures show, the background subtracted y-ray time spectra fit to Equation 4.9, so a value for the flat background could be extracted. After the background subtracted y-ray data were rebinned, and divided by the background subtracted electron time spectrum, an inconclusive result was found. This is shown in Figures 5.8 and 5.10 for two such y-rays. Clearly, if one wants to look for a hyperfine effect one needs much better statistics by at least an order of magnitude at a lower muon stop rate.  114  3 6 8 4 keV rebinned by 50 J  :  I  I  600  i  plotdata fit C 3 9 6 . 5 4 7 5 ± 98.24736 D 0.0003184624 ± 0.0002461195 . ' B 85:1779 ± 119.4304  500 •  •  i  40 0  §.300 o o 200 100 0 .0  :  ' 1000  2000 3000. 4000 . • Time (ns)  5000  6000 : •  7000  FIGURE 5.7: THE BACKGROUND SUBTRACTED TIME SPECTRUM FOR THE 3684 K E V Y-RAY.  Ratio -of. 3 6 8 4 to e— time -L  J  spectra i  i  0.004 A  10.002-  o o o  .20.000  -0.002 0  1000  2000  3000 4000 Time (ns)  5000  6000  FIGURE 5.8: THE RATIO OF THE 3684 KEVY-RAY TO THE ELECTRON TIME SPECTRA.  7000  4 4 3 9 keV rebinned by 50 400  300  C/3  C  plotdata's f i t C 114.6986 ± 80.03414 D 0.00140525 ± 0.001556316 B 107.9736 ± 15.08312  H  200  3  o o  100 0 4  .OH i  0'  i  1000 2000  :  1  1  3 0 0 0 .4000 Time (ns)  :  r  1  5000  6000  7000  F I G U R E 5.9: T H E B A C K G R O U N D S U B T R A C T E D T I M E S P E C T R U M FOR T H E 4 4 3 9 K E V Y - R A Y  Ratio of 4 4 3 9 to e— time s p e c t r a 0.0010 -1 L' 1 " L  0.0005 H 0.0000 H -0.0005  -0.0010 H -0.0015  i r 1000 . 2000  r. 1 3000 4000 Time (ns)  1  5000  :  —r 6000  FIGURE 5.10: T H E RATIO OF T H E 4 4 3 9 K E V Y - R A Y T O T H E E L E C T R O N T I M E S P E C T R A .  7000  5.4 The y-ray Yield Results Using the methods outlined in Section 4.8 the yields of the C and C y-rays l3  l 4  were obtained. Table 5.9 shows the results for the C y-rays obtained from both l 3  detectors. These results have not been measured before and are consistent between detectors except for the 3089 keV y-ray, which is not seen in Ge2. This non-observation is due to the fact that Ge2 is less efficient than Gel and that the 3089 keV peak is Doppler broadened, making it hard to distinguish from the background, unlike the 3853 keV peak which is not Doppler broadened. As discussed in Section 2.5, this 3089 keV level has also been seen in low energy N(p,d) N reactions, and occurs because of a l4  13  slight configuration mixing of the N ground state, or because of complications from the 14  reaction mechanism.  *  Table 5.9: The C y-ray yield results. 13  y-ray Energy • (keV) 169 595  Gel yield/ captured u"(%) Below Threshold Overwhelmed by  Kn,n')  127  764 3089 3683 3853  <0.20 1.5± 0.6 6.5+2.1 1.9+0.7  Ge2 yield/ captured , u"(%) Below Threshold Overwhelmed by  Average yield/ captured u~ (%) Below Threshold Overwhelmed by  <0.42 Not seen 5.1+ 1.4 2.0±0.7  < 0.20 1.5± 0.6 5.8+1.3 2.0+0.5  Kn,n')  127  Kn,n')  127  Table 5.10 shows the y-ray yields per captured muon for C . These results are l4  only from Gel, since the acceptance of Ge2 was too low. The only previous  117  measurement was by Giffon[ ] and his result for the 7010 keV peak was (6.7 ± 1.0) % 79  which does not agree with this experiment. Note in this experiment the 7010 had on it a small contamination peak from Cl(n, y). The area of this background peak was j:>  estimated by the use of the acceptance of the detector, the branching ratio of the y-ray, and by the areas of the other "Cl(n, y) peaks. That estimated area was then subtracted from the 7010 total area. Table 5.11 shows the y-ray yields per captured muon for C and B . These y12  l0  rays are emitted when the muon captures on N , then the resulting nucleus emits two 14  neutrons ( C) or two neutrons and a deuteron ( B). These results are only from Gel. It 12  10  is assumed that there are background processes which could produce the C y-ray. If one 12  looks at the time spectra of the y-rays (Figures 5.7 and 5.9), one sees that this C y-ray 12  has a much higher background than the C y-ray. One could estimate that only about l 3  25% of t h e ' t y-ray is real signal. This is a very uncertain estimate. Applying this estimate to the raw yield of this C y-ray (3.1 ± 1.9), one finds that about 1% of the time 12  this C y-ray is radiated. However this y-ray is not seen in other muon capture ,Z  experiments with the same setup[ ]. The y-rays from B are seen, but could be 120  1 0  background lines. Table 5.12 shows the y-ray yields per captured muon for Be, B , and B . 10  12  13  These y-rays would be emitted when the muon captures on N , and the resulting nucleus, 14  14  C, emits an alpha particle, deuteron, and a proton respectively. No y-rays were seen  from any of these processes. So only upper limits were given. These results are only for Gel.  118  Table 5.10: The C y-ray yield results. Gamma Energy Yield/captured p" in (%) 495 < 0.048 613 < 0.12 634 < 0.14 808 <0.50 918 <0.29 (probably -0.05) 1248 Hidden by Ge(n,y) 6092' 1.3 + 0.6 6726 1.3 ±0.5 7010 3.4 ±1.4 7339 < 0.068 This is the entire peak (Doppler plus Gaussian components). 14  ~able 5.11: The C and B y-ray yield results. Gamma Energy Yield/captured p" in (%) 718,3 < 0.12 ±0.04" 1021.7 < 0.13 ±0.07**' 4438.03 l.±| 12  10  Nuclide i o  B  ,2  C  These peaks are seen but they could be background lines.  Table 5.12: The Be, B , and B y-ray yield results. Gamma Energy Yield/captured p" in (%) 219.4 < 0.047 2592.6 < 0.15 2811 <0.16 3367.4 Hidden by C double escape 5955.4 ' < 0.034 720.34 Hidden by B 947.11 < 0.057 953.10 <0.27 2722.7 < 0.01 418 ' Hidden by I(n,n'y) 596 Hidden by I(n,n'y) . 3482 <0.17 3713 • < 0.044 . 4131 <0.62 10  12  13  12  1U  Nuclide Be Be Be Be Be lu  10 10 lu lu  B B  U  ll  12 12  127  l j  127  1J 1J , J iJ  B B B B B B B  .  5.5 The Nuclear Level Yield Results Figure 5.11 shows the nuclear level diagrams for C . By using the branching l j  121  ratios[  ] from this diagram and the results of Section 5.4, the percentage of the time in 14  1  1  which a muon capture on N produces a particular level in C can be found. In other J  words, the nuclear level yield can be found. Table 5.13 has these results for C . l j  able 5.13: The nuclear level yields of C . Level Energy (keV) Level Yield/ captured u" (%),'• 3853 3.1+0.8 3684 4.7+1.3 3089 1.4 ±0.7 l3  The Doppler fit of the 3684 keV y-ray tells us that (15.9 ± 1.0) % of that y-ray's area is fed from the level above. This cascade percentage caii also be calculated by the use of the values in Table 5.13, and the branching ratio of the 169 keV y-ray, as indicated in Equation 5.1.  Cascade  where  BR|69  = (  ^  BRm  ^  LY  ,  .  .  .  (5.1)  ;  ;"'  is the 169 keV yrray branching ratio, LY3853 is the level yield of the 3853  keV level, and yL3684 is the 3684 keV y-ray yield. The result of this calculation is (19 ± 8) %, which is consistent with the Doppler fit method.  120  Figure 5.12 shows the nuclear level diagram for C , with its y-ray branching 1 4  ratios [ ]. Since not all of the y-rays in C were observed, not all of the level yields can l06  l4  be obtained. The yields for the 7341 keV, the 6904 keV, and the 6589 keV levels will only be upper limits. Since these levels feed either of the 6094 keV and the 6726 keV levels, the yields of these levels cannot be found exactly. For these yields instead of subtracting off the contribution of cascades from the levels above them, that component was put in the systematic error (last error listed). This was because the actual amount of cascade was not known, only an upper limit. Table 5.14 gives the yields for these levels. The 6092 keV y-ray from the 6094 keV level has interesting structure because of cascade feeding. By using the two Doppler fit models to the full energy peak (from Section 4.5), which model the cascade into the 6094 level as pure Gaussian, the level yield can be estimated. The average of these three models implies that (8.6 ± 5.3) % of the full energy .6092 keV y-ray's area is from cascade. The same value obtained from fitting the 6092 keV single escape peak, is (15 ± 12) %. In the fit to this single escape peak, there is ho evidence of a second Doppler broadened peak on the original one. This argues against cascade from the 7341 keV level. Applying the weighted average of these two results (10 + 6)% to the y-ray yield from Section 5.4, it is found that the 6094 keV level yield per captured muon is (1.2 ± 0.6) %, which is in agreement with the value in the table obtained by the method of the last paragraph. The full energy cascade percentage also implies that (0.12 ± 0.08) % per capture would be a cascade from a higher level, which has a long lifetime. Now we know that the 6728 keV level is populated, and would cascade contributing (0.05 ± 0.02) % per muon capture. The 7012 keV level contribution to the cascade will be Doppler broadened, so that would leave  121  (0:07 ± 0.08)'% feeding from the 6589 keV level, which is in agreement (within errors) with the non-observation of the 495 keV y-ray. A feeding of 0.05% (BME model) or 0.02 % (POT model) is expected from the Mukhopadhyay model, by scaling the capture to the 6589 keV level to be 1.5% or 0.68% of the 7012 keV level. The BME model prediction for the feeding is nearly inconsistent with the upper limit listed in Table 5.13, whereas the POT model prediction is consistent. The 7012 keV level yield of (3.4 ± 1.4) %o does not agree with the theoretical yield presented in Section 1.7 in Table 1.9 viz 28% for the model which does not use the 2  2  (2s-ld) theoretical model, and 14% for the (2s-ld) model. Both of these models assume that the hyperfine transition rate is zero, in their calculations. It would be interesting to see a calculation with the Ishida et al.[ ] hyperfine result used, as this type of calculation 30  might resolve the discrepancy. Both theoretical estimates seem too high, especially when comparing to the (u",y) reaction. Our value of (4.8 ± 1.4) % for the sum of the three levels (6728, 6903, 7012) compare favourably with the (TI\Y) result of (6.22 ±0.40)%. Table 5.15 gives the level yields for B and C. As one can see the 718.3 keV 10  12  level is completely fed by the 1740.15 keV level. Table 5.16 gives the level yields for 13  1 0 1 2 lu  Be, "B,and  '  B. In the case of this table, the amount of cascade from above was not  subtracted since the y-rays were not observed. The 2592 keV y-ray was not listed because the branching ratio for that y-ray is not currently known. The average of the results, for the 7012 keV level from this experiment and from the work of Giffon et al.[ ] is about 5.1%. Normalized to that value and then summed 79  the results from Tables 5.13 and 5.14, imply that (9 ± 2) % of the muon captures are to a bound excited state in C and that (14 ± 3) % of the muon captures are to a bound, 14  .  :  .  122  excited state in C. If one assumes that the levels fed in the N(y,p) C reaction are in 13  l4  13  the same ratio as those for N(u~,vn) C, then Table 2.4 and the (14 + 3) % muon capture l4  l3  to C , can be used to estimate the rest of the muon capture yield. This hypothesis can be l3  justified by the fact that Miller et al.[ ] found such a similarity for muon capture in S i . 122  The amount to the  28  C ground state would then be (46 ± 8) %. The unbound 7.55 MeV  13  12  level in C would go to the  C ground state since there would not be enough energy to  go to the 4 4 MeV excited state of G. Table 2.4 then implies that (39 ± 7) % of the 12  :  muon capture goes to the ground state of C . Adding up all of these contributions, one l2  finds a total of (108 ± 12%). So, clearly the muon capture yield to the 7012 keV level could not be as high as the values of 14% or 28% calculated by Mukhopadhyay[ ]. 74  123  Table 5.14: The.nuclear level yields of C . Level (keV) y-ray used 7341 • 613 7339 7012 918 7010 6903 808 6589 495. 6728 634 6726- • l4  6094  6092  Level yield/captured u" (%) < 0.35 <0.42 <20 3.4 ±1.4 < 0.50 . < 0.049 <3.9 1.40 ± 0.49 ±.° 12  .  1.3±0.6±°  Table 5.15: The nuclear level yields of B and C . Level (keV) y-ray used Level yield/captured u" (%) 718.35 718.3 -0.01+0.25 1740.15 1021.7 . < 0.13 ±0.07". 4438.91 4438.03 i± .. 10  ,t  :  1  —  79  l2  Nuclide • B io . C IU  B  I2  1  These peaks are seen but they could be background lines.  Table 5.16: The nuclear level yields of Be, B , and B . Level (keV) • y-ray used Level yield/captured p" (%) 5958.39 5955.4 < 0.034 6179.3 219.4 . <0.20 2811 < 0:21 953.14 •• 953.10 <0.27 2620.8 947.11 < 0:41 2723 2722.7 < 0.01 3483 . . 3482.6 < 0.17 3713 3713 < 0.048; 4131 4131 < 0.91 10  12  l3  Nuclide B ,o .o B 1U  B  B  12  B  U  B B B B  12 ,J , j U  .  124  1 3  c  /v> no- " V  v  5/2+ 3/2-  3853.807 8.60 ps 3684.507 1.10 fs  1/2+  5  1/2-  3089.443 1.07 fs  0.0 S T A B L E  FIGURE 5.11: THE NUCLEAR LEVEL DIAGRAM OF C . , 3  125  14  C  22±_ 0^_ "t>T  Q±_  7341 7012 .6902.6 6728.2 .6589.4 6093.8  111 fs 9.0 fs' 25 fs 66 ps 3.0 ps <7fs  0.0 5730 y  Q±_  FIGURE 5.12: THE NUCLEAR LEVEL DIAGRAM OF C . L 4  126  Chapter 6: Conclusion Measurement of the muonic hyperfine transition rates via neutron detection was performed. In the cases of LiF,  (CF2) , n  Al, LiAlFL, LiCl, and CC1 the hyperfine 4  transition rates confirmed previous results and agreed with the theoretical predictions. The F rate is the most accurate result to date. In the case of Na and NaH the results did l9  not agree with theory nor with previous results. With regard to the discrepancy with previous experiments, it could be possible that the large data collection rate of the previous experiments could effect the muon time spectra. In the case of P the previous experiments gave conflicting limits on the hyperfine transition rate, but no actual value. The results of this experiment agree with one of these limits but disagree somewhat with the theoretical prediction. An important result is that there was no evidence of a chemical effect on the hyperfine transition rate when comparing metal and hydrides (Na, NaH: Al, LiAlH4).  Similarly for fluorine, the rates in LiF and ( C F 2 ) are the same. These are novel n  and interesting observations. The capture rate asymmetries were also measured and it was found that they tended to agree consistently with the Primakoff calculations unlike the other calculations. The Primakoff calculation of these asymmetries was not done for Na. It would be interesting to compare the results of this experiment with the Primakoff calculation of the capture rate asymmetries seeing that there is a discrepancy in the Na hyperfine transition rates. Results were obtained for K and Cl, but because the asymmetries were very small, it was hard to determine a reliable hyperfine transition rate.  127  A search for a hyperfine effect in N was also performed using two experimental techniques. In the case of the neutron detection technique, the lifetime of the muon in N was found to be different in the neutron time spectrum than in the electron time spectrum by about 36 ± 8 ns. This indicates that the upper hyperfine level has a higher capture rate, which explains the discrepancy between the lifetime measurement of Suzuki and the lifetime measurement of Martino. In the control measurement on water the difference of 15 ± 13 ns was practically consistent with zero. In the y-ray experiment, the background subtracted y-ray time spectra were divided by the background subtracted electron time spectrum was limited by statistics, so its results were inconclusive. It is entirely possible that the p.SR hyperfine transition result is an unaccounted for depolarization effect. The y-ray experiment also yielded extra useful information. The nuclear level yields in C , C , C, and B were found. Previously only one of these yields had been 14  l3  12  10  measured. The results of this experiment disagree with the previous measurements and previous theoretical calculations. In the theoretical calculation the hyperfine transition rate was not accounted for in the calculation of the yield, since it was measured years after the calculation; including it may resolve the discrepancy between theory and all the experimental measurements. In addition, the original calculation gives an unrealistic yield per capture. In addition the energy of two y-rays in C were measured to better 14  precision than before. These two y-rays are at 7016.8 ±1.3 keV and at 6730.6 ± 1.0 keV. It is clear that improvement on our results is possible with presently available equipment; however better statistics are the key and the time required for the experiment would be significant and unlikely to be allocated. This is compounded by the fact that the rates in this experiment were higher than the ones in the ideal conditions, lower rates  128  i m p l y e v e n longer data taking times. A s T R I U M F has a 100% duty c y c l e e f f e c t i v e l y for this type, o f experiment, a n e w accelerator w o u l d not help. T h e e n i g m a o f the h y p e r f i n e effect in  l 4  N unfortunately remains. 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